herself as a man, Portia is, ironically, able to showcase her real talents as a lawyer. Shakespeare seems to be saying that sometimes it takes appearing as something we are not to show who we really are.

Portia and Nerissa, disguised as a lawyer and a clerk, also insist that Bassanio and Graziano give them rings they received from Portia and Nerissa that they promised never to part with. The men give up the rings reluctantly and only out of deep gratitude to the twosome for saving Antonio. However, they are once again deceived by appearances, for unbeknownst to them, they are giving the rings back to their beloveds.

Antonio suffers from the difference between appearance and reality. He seems both prosperous and secure with three ships out to sea, and so he doesn't worry about the loan he has taken out with Shylock. A grim reality appears for a time to take over when all his ships seem lost at sea: but as with the rings, reality is not as it appears, and Antonio's ships do come to port.

Shakespeare depicts reality as a slippery business, full of twists and turns that can deceive, though in this comedy all works out well in the end, at least for the principal Christian characters.

I would add to the excellent answer above that Portia's decision to disguise herself as a man in act IV of Shakespeare's The Merchant of Venice can illuminate even more about the theme of appearance vs. reality in the text. Portia's donning of the disguise is an expression of this theme made physical: she is not what she appears.

Portia takes on this disguise so that she will be able to defend Antonio, her husband's dear friend, in a court of law. That she must pretend to be a man to do so is symptomatic of society at the time. Portia is just as intelligent and capable as "Balthazar" (her alter ego), yet only Balthazar is taken seriously.

Portia uses her necessary deception to her advantage by testing her husband's loyalty to her while interacting with him as someone else. Act V of the play, after all of the Shylock drama has concluded, deals largely with the aftermath of Portia and Nerissa's deception. Both women use their knowledge of their husband's actions while in Venice—which their husbands don't know they know—to their advantage. The comedy in the scene stems from dramatic irony. The audience, Portia, and Nerissa all know that things are not as they appear.

In The Merchant of Venice, the theme of appearance and reality is prominent because many of the characters are not what they seem and their actions are sometimes contradictory to their seemingly honest motives. Furthermore, the caskets that hold the secret to a successful marriage to Portia mislead her suitors and they choose poorly.

1. Shylock appears to be willing to loan money to Antonio even though he "hates him for he is a Christian" (I.iii.37). However, the penalty if Antonio cannot repay him is unreasonable and whereas it is not taken literally by the Christians, it is meant literally by Shylock when he demands his "pound of flesh."

2. Antonio appears to be virtuous and generous. He loves his friends and has a good reputation. Yet he treats Shylock very badly simply because he is a Jew which makes him a hypocrite. Shylock reminds the reader that it is Antonio's double standards that have led to this situation. Shylock refers to "the villainy you teach me" in Act III, scene i, line 61 meaning that Christians like Antonio are responsible for the animosity (hatred) between them.

3. Portia's suitors must choose from three caskets of gold, silver and lead if they desire to marry her. Portia is relieved that most of her suitors to date have chosen foolishly as they have been misled by the words which describe the contents of the caskets. Only one has Portia's portrait inside but so far the suitors have not realized that there is a warning contained in the words that read "All that glisters is not gold" (II.vii.65). Only Bassanio will choose wisely and there is still debate as to whether Portia guides his choice (which would be forbidden by her father's will) or whether he makes his own considered choice.

4. Even Jessica fools her father and runs away with his precious ring, selling it and therefore revealing that she has no respect for Shylock. 

5. The actions of the characters have been quite selfish and the theme of appearance versus reality has shown these traits but Portia will show great "mercy" and compassion when she disguises herself and helps Antonio avoid what would have been certain death if he had allowed Shylock to take his bond of a "pound of flesh." 

Shakespeare then reveals the theme through character development and this helps drive the plot and subplots forward. 

In act 3, scene 2, Bassanio demonstrates his ability to distinguish between appearance and reality when deciding which casket to select in hopes of winning Portia's hand in marriage. When Bassanio examines the gold casket, he states that appearances are often deceiving and proceeds to list several real-world examples which support his (valid) argument.

Bassanio begins by mentioning that a person can conceal their own evil in a court of law by speaking with a "gracious voice," and says that a "damned error" can be covered over with the nice show of a blessing and some scripture to justify it. He then reiterates that appearances can be misleading by stating,

There is no vice so simple but assumes Some mark of virtue on his outward parts (3.2.83–84).

Bassanio continues to give real-world examples of deception by mentioning that many cowards resemble Hercules or Mars but "have livers white as milk" and are easily frightened. He also notes that women often use cosmetics to appear much more beautiful than they really are and their lovely wigs are also deceiving. Bassanio once again elaborates on the dangers of trusting outwards appearances by stating,

Thus ornament is but the guiled shore

To a most dangerous sea, the beauteous scarf

Veiling an Indian beauty—in a word,

The seeming truth which cunning times put on

To entrap the wisest (3.2.99–103).

After Bassanio's speech, he cleverly refrains from picking the gold or silver caskets and chooses to open the box made of lead, which contains Portia's portrait and a scroll that summarizes his fortune. Overall, Bassanio is able to distinguish between appearances and reality by noting several real-world examples regarding the dangers of trusting external appearances.

The theme of appearance versus reality is prevalent in The Merchant of Venice. One of the ways to examine this is by looking at the relationships between many of the characters in the play. Most obvious is Portia's disguise and subsequent interactions with the gentlemen of the court, in order to save her suitor's friend Antonio from Shylock's wrath in collecting his bond. Another example is the appearance of Jessica's devotion to her father Shylock, which is underscored by her desire to flee his grasp. The manner in which she accomplishes this, coupled with what she does once she has, highlights this theme.

There are other more subtle instances of appearance versus reality as well. Towards the end of the play Portia and Nerissa are complicit in a scheme to test their new relationships with Bassanio and Graziano. Also, Antonio's willingness to enter into a bond with Shylock, a man he despises, on the surface appears to be done out of freindship. Another possible interpretation is that Antonio is trying to live vicariously through the exploits of his younger  companions and gain entry to the life promised by Belmont.

To address the question of how the Merchant of Venice deals with the theme of appearance versus reality, start by reviewing the play. To be specific, look at the following things:

Look at how Antonio acts towards Shylock when talking directly to him, versus how he acts when Shylock can't hear him.

Then do the same for Shylock. What does he say privately, versus publicly?

Then, consider Portia. She dresses up like a man, changing her appearance, in order to change reality. Look at that section.

Then look at the discussions of the laws. What do they mean--and what are they interpreted to mean?

Then look at which chest is considered the right choice, versus which one different people choose. There is a conflict there between appearance and reality.

Remember this line from the play: All that glisters is not gold.

There are many ways in which the play explores this question. One example occurs when Portia's suitors try to answer the riddles of the caskets. The first one, the gold one, states quite clearly "all that glitters is not gold; often have you heard that told." Choosing the gold casket, thinking it holds riches, reveals that appearances can be deceiving and that true value is not determined by accepted standards of worth. Ultimately the casket that holds the key to Portia's hand is made of lead, and Bassanio knows to choose this one.

Shakespeare is trying to tell us that surface appearances deceive and that there is deeper reality hidden beneath the way things or people appear.

For example, disguised as "Balthazar" in the courtroom, Portia appears to be a male lawyer, but is, of course, a woman. In the same way, her "Clerk," who also seems to be male is, in reality, her female servant Nerissa. Their gender bending surface appearances mask the deeper reality (unacknowledged in that time period) that women were just as capable of being lawyers and arguing persuasively as men. In fact, Portia argues eloquently for mercy towards Antonio and wins his freedom from having a pound of flesh cut from his body. But without projecting the illusion of being male, she could not have saved Antonio.

In having a woman competently defend a male, Shakespeare suggests to his audience that the appearance in his society of women as weaker and less capable is not reality. He thus invites to look beneath the surface of people to see who they really are.

Likewise, in choosing the correct casket for Portia's hand, the winning suitor must realize that "All that glisters is not gold." The gold casket may look most attractive on the outside, but it will not win Portia's hand. One, the other hand, the lead casket does not appear attractive on the outside but represents inner beauty—Portia's picture is inside. It states "Who chooseth me must give and hazard all he hath," showing that sacrifice is the way to win the heart of a beloved, not money or outward appearance.

Shakespeare is trying to say that, despite surface appearances, what matters most in the world are traits such as mercy, a willingness to sacrifice for others, love, loyalty, and friendship. Perhaps Bassanio didn't need to borrow money to project the illusion of wealth: perhaps what really mattered was his heart.

You might look at Shylock too. Beneath his anti-Semitic portrayal, even he has a heart: he grieves, for example, when his daughter Jessica elopes with a Christian.