Juliet speaks here. She has just asked her nurse to identify a certain young man she finds attractive. He is attending the Capulet ball, but she doesn't know who he is. The nurse tells her that he is Romeo, of the hated house of Montague. The Capulets and the Montagues have been feuding for so long that nobody knows what their argument is about anymore, but they all know that they hate each other.
Juliet knows she is supposed to hate any Montague. However, she has just realized the only person she loves happens to be a Montague. That's what she means when she says "My only love sprung from my only hate!" How can she love a member of a family she hates? This is what is known as a paradox or contradiction.
When she says "too early see unknown, and too late known!" she is saying that she gazed on Romeo too long before she knew who he was to hate him now. She has discovered too late who he is. She can't switch to hating him, even if he is a Montague, because Cupid's arrow has already hit her, and she is in love.
In modern life, we can also fall in love with a person that we later find out we have a reason to hate. An Israeli and a Palestinian could fall in love with each other, even though the two groups are feuding over the West Bank of Israel, if the two didn't grasp right away that they were supposed to be enemies. The lesson for modern life is that we should judge people for who they are individually rather than judging them based on what group they happen to come from.