Why did Shakespeare begin The Tempest Scene 1 with a storm?

What is the significance of the title The Tempest?

Some Shakespearean scholars and critics, including Hallett Smith and Frank Kermode, suggest that the title of Shakespeare's last fully Shakespeare-written play should be The Island, or Prospero's Island, rather than The Tempest. They argue that the storm at sea occupies only one scene in the play, whereas the island itself remains constant throughout the play and is the location for all of the action in the play.

However, The Tempest isn't about the storm at sea. The raging tempest is simply an illusion that Prospero uses to deceive his intended captives and to bring all of those onboard the ship onto his island so he can manipulate and control them. Prospero shipwrecks his enemies and forces them to his island in much the same way that Prospero and his daughter, Miranda, were cast adrift and landed on this island twelve years ago, for which he intends to avenge himself against his enemies.

Rather than referring to the storm—which doesn't truly exist—the title is symbolic of the turmoil between, among, and within the characters themselves and the multiple subplots which compete for the audience's attention. There's no character in the play who isn't at odds at one time or another with another character or group of characters. Even Miranda, ever the loving daughter, is at odds with her father for bringing the violent storm against the ship and everyone aboard it.

MIRANDA. If by your art, my dearest father, you have
Put the wild waters in this roar, allay them.
... O, I have suffered
With those that I saw suffer! A brave vessel,
Who had, no doubt, some noble creature in her,
Dashed all to pieces!
(act 1, scene 2, lines 1–8)

Prospero assures Miranda and the audience that it's all an illusion.

PROSPERO. Be collected.
No more amazement. Tell your piteous heart
There's no harm done.

The direful spectacle of the wreck, which touched
The very virtue of compassion in thee,
I have with such provision in mine art
So safely ordered that there is no soul—
No, not so much perdition as an hair
Betid to any creature in the vessel
Which thou heard'st cry, which though saw'st sink.
(act 1, scene 2, lines 14–16, 30–37)

No one was hurt by the storm or the shipwreck. In fact, Prospero does nothing to the involuntary guests on his island except frighten and confuse them with magic and illusions, humiliate Alonso, Sebastian, and Antonio—who Ariel calls the "three men of sin"— in the banquet scene, and thwart the doomed-to-fail assassination plot initiated against him by his slave Caliban, and Caliban's cohorts, Trinculo and Stephano.

The Tempest is ultimately a play about the self-discovery, forgiveness, reconciliation, and reunion that arise from by the spiritual turmoil of the characters who were brought together by the illusion of a storm.

Prospero forgives and reconciles with his primary enemies, Alonso, the king of Naples, and Prospero's brother, Antonio, who usurped Prospero's dukedom of Milan twelve years earlier. Alonso agrees to the marriage of Miranda and his son, Ferdinand. Ariel receives his long-promised and long-delayed freedom. As the others sail away to Milan, Caliban is left once again the master of what was originally his own island.

Finally, as Prospero promised, when all of these things are accomplished, Prospero frees himself and everyone else from his magic.

PROSPERO. And, when I have required
Some heavenly music—which even now I do—
To work mine end upon their senses that
This airy charm is for, I'll break my staff,
Bury it certain fathoms in the earth,
And deeper than did ever plummet sound
I'll drown my book.
(act 5, scene 1, lines 56–62)

What is the significance of the title The Tempest?

A tempest is a violent storm and considering that the first scene of the play takes place in such a storm, the title is quite fitting. It is this tempest, caused by Prospero's magic, that results in the entire plot and action of the play.

There is a symbolic meaning to the play's title as well. The relationships between many of the characters are as chaotic as a violent storm. Nothing goes smoothly for anyone, even the would-be puppet-master Prospero. He has to endure a mutiny that nearly throws all his plans awry.

Antonio's true motivations are laid plain to the King of Naples. The King for his part is distraught over the feared loss of his son. Almost nobody respects Gonzalo, despite his wisdom and optimistic outlook. Throughout all of this, we see Prospero's extreme anger towards his brother building before eventually subsiding as a storm does.

As we can see, the literal tempest exposed a the underlying stormy relationships between nearly every character in the play. In this sense, it is a very appropriate title.

What is the significance of the title The Tempest in terms of symbolism, imagery, and Shakespeare's time?

The Tempest starts with an actual storm, or tempest, created by Ariel to bring ashore to the island the men who helped Antonio usurp the throne that belongs rightfully to Prospero. The imagery of the ship in the storm is of a vessel that the high seas and violent winds have torn asunder. As the ship is about to go down in Act I, scene 1, voices cry out:

"Mercy on us!—We split, we split!—Farewell, my wife and children!—Farewell, brother!—We split, we split, we split!" (lines 36-38)

The image of the ship being torn apart has a symbolic meaning as well, as the ship of state (referring to the government) is about to be torn apart too. Antonio, who has wrongfully usurped the dukedom, is eventually to be unseated in favor of Prospero, the rightful duke. The storm is a symbol for the coming dissolution of the current political structure. 

The significance of The Tempest in Shakespeare's time is that it was written in 1610, a year after the British first colonized Virginia. A ship called the Sea Venture was wrecked during a storm off Bermuda in 1609 during the third supply mission to the new colony of Virginia, and its wreck is believed to have inspired Shakespeare to write The Tempest. 

What is the significance of the title The Tempest in terms of symbolism, imagery, and Shakespeare's time?

This title can be understood on both a literal and symbolic level. First of all, the literal definition of a "tempest" is a violent disturbance, sometimes related to weather, sometimes related to other upsetting commotion.

As the play begins, we meet the magician Prospero (ex-Duke of Milan), his lovely daughter, Miranda, the spirit of the winds, Ariel, as well as other spirits who live on a tropical, enchanted island. Prospero and the spirits battle a ship at sea transporting enemies. The enemies scatter over the island. The Price of Naples, Ferdinand, meets Miranda and falls in love with the handsome prince.

Thus, the tempest is literally the storm, and symbolically the disruption of the enchanted life of seclusion that Prospero has enjoyed.

As for the "effect of the era," Shakesperian scholar Stephen Greenblatt says the "Shakesperare's contemporaries were fascinated by the figure of the "magus" the great magician who by dint of deep learning, ascetic discipline and patient skill could command the secret forces of the natural and supernatural world." Though feelings about the occult were mixed, people were interested. Therefore, it is not surprising that characters like Prospero and Ariel crop up in the Renaissance.

What is the significance of the beginning and ending of The Tempest?

The play opens with a violent storm at sea that leads a ship filled with important personages to shipwreck on a deserted island. As we find out in act 1, scene 2, this storm was the first step in Prospero's plan to revenge himself on the people who betrayed him and stole his kingdom. Prospero's enemies usurped his kingdom and put he and his very young daughter, Miranda, out to sea in a leaky vessel. Now, however, Prospero, formerly the duke of Milan, has his chance for payback against his brother Antonio, who stole his dukedom, and Alonso, the king of Naples, who worked with Antonio to betray him. Prospero, with his skills in magic and the magical sprite Ariel under his command, has a strong advantage over his captives.

However, by the end of the play, having confused, accused, and scared his enemies, Prospero has a change of heart. This occurs when Ariel expresses his pity at how frightened the shipwrecked people are. Prospero feels that if a mere sprite, who isn't human, can feel mercy for his captives, he, too, should take the higher path. Prospero decides to do what is rarely done to enemies in one's power: he forgives them and sets them free. He even forgives Antonio, the chief villain, despite Antonio's lack of remorse.

The play shows a movement from vengeance to forgiveness and makes it clear that in his final act of mercy, Prospero has found his better and higher self.