This quote is from Act 3, sc. 1 and it is spoken by Bottom to Titania. Puck, seeing that Bottom was acting like a fool, turns Bottom's head into the head of a donkey. Titania has fallen immediately in love with Bottom upon waking because Oberon annointed her eyes with the juice from the flower. Bottom is unaware of his transformation and is confused about Titania's attentions, so he delivers the line in question. The quote is one of the underlying ideas of the play - that love sometimes occurs without reason. People don't always use common sense when it comes to love because emotion takes over. In Act 1, sc. 1, Lysander says that "The course of true love never did run smooth." This, again, means that logic doesn't always have anything to do with love because emotions aren't necessarily logical.
The line is spoken by Bottom in William Shakespeare's "A Midsummer Night's Dream" Act III Scene 1. The full quotation is:
[Bottom:] Methinks, mistress, you should have little reason for that. And yet, to say the truth, reason and love keep little company together nowadays.
I've always assumed that it means the same as another Shakespeare quote, "love makes fools of us all."