This quotation from act 1, scene 1 of Shakespeare's A Midsummer Night's Dream ironically sets the tone for the entire play. It is spoken by Helena, who is in love with Demetrius (although Demetrius is in love with Hermia). Helena means that true love doesn't care all that much about what the beloved looks like. This is why Cupid, the god of love, is portrayed as blind. Lovers decide whom to love based on all the qualities of the beloved and not on appearance alone.

Of course, in this play, the exact opposite is true, and that's what makes this quotation both ironic and hilarious. When fairy king Oberon wants to play a trick on his wife, Titania, he sends his servant Puck to find a magical flower. If anyone spreads the juice from this flower on the eyelids of a sleeping person, he or she will fall madly in love with the first person he or she sees upon awakening.

Oberon notices how badly Demetrius treats Helena and how much Helena loves Demetrius, so he decides to help the young lady out. He tells Puck to put some of the flower's juice on the eyelids of a young Athenian man so that he will fall in love with the young woman with him. Puck, however, gets mixed up and puts the love potion on Lysander's eyelids instead. Lysander sees Helena upon awakening and falls in love with her, leaving his true beloved (and fiancée) Hermia confused and upset when he goes off to chase Helena. Puck then tries to fix his mistake and puts some of the potion on Demetrius' eyelids as well, making Demetrius also fall in love with Helena.

Thus in this play, love is far from blind. It appears as the direct result of seeing another person (at least if the seer has love potion on his eyelids). What's more, love has nothing at all to do with the mind, but rather with Puck's magical flower and clumsy ways. Helena's words about love not looking with the eyes but with the mind turn out to be hilariously ironic indeed. In the end, though, Puck finally sorts everything out, and both couples, Demetrius and Helena and Lysander and Hermia, marry and presumably live happily ever after.

Shakespeare writes about love a lot.  This quote is about that theme, but what I like about this quote is that it doesn't support the "love at first sight" notion.  In fact, the heroic couplet takes sight completely out of the love equation.  Shakespeare is telling his audience, through Helena, that love is a matter of the heart.  It is more dependent on an emotional bond rather than a physical attraction.  The idea is nothing new to Shakespeare.  He writes about the same thing in a couple of his sonnets.  Sonnet 130 explains how his mistress is definitely not attractive, but he still loves her deeply.  

And yet, by heaven, I think my love as rare

As any she belied with false compare.

Sonnet 141 is along the same lines; however, it specifically mentions the eyes just like Helena does in the play. 

In faith, I do not love thee with mine eyes,
For they in thee a thousand errors note; 
But 'tis my heart that loves what they despise,
Who in despite of view is pleased to dote....

As a general rule of love, I feel that the quote is teaching an important lesson.  In terms of the play, the line foreshadows events to come.  Most notably, the line foreshadows Titania falling in love with Bottom despite the fact that he has a donkey's head.  

Another example of how this quote shows true love being blind can be found through the character of Demetrius. When the play begins, he's in love with Hermia, and Helena indicates that the main reason is because Hermia is prettier.  By the end of the play, Demetrius has found his true love in Helena.  He was looking for love with his eyes; however, he wasn't finding true love.  As soon as he stopped relying on his eyes, he was able to discover the love that he and Helena share.  

This quote is important for a couple of reasons.  First, it is an example of a heroic (or rhyming) couplet--two lines of poetry that have end rhyme. 

As for the meaning, the quote is important because it represents one of Shakespeare's many ideas about love, and Shakespeare is often considered to be an expert at getting to the heart of human emotions.  This quote is basically the adage, "Love is blind."  What he means is that if you love someone, you generally love them not for what they look like, but for who they are inside.  Out of context, the quote is quite romantic.  In the context of the play however, the quote is quite ironic; later Titania will fall in love with Bottom after he's been given a donkey head.  Bottom's character is not admirable, so there is really no reason--heart or mind--for her to love him, and that's where irony enters the situation.