If you want the full summary, go to the enotes link provided. If you want my five minute version, here it goes!
Romeo wants to see Juliet again so he ditches the rest of his crew that came with him to the party. He climbs over a wall and ends up in the Capulet orchard. Of course, Juliet on her balcony, thinking aloud the value of names. Romeo wants to jump in but is struck by her beauty and lets himself listen to Juliet. Juliet mentions that she wishes Romeo could lose his name. At this point Romeo scares the life of out his love by agreeing with her.
After Juliet (quickly recovering from her scare) warns Romeo that being in the garden is not a good idea right about now, the two begin to talk about their love for each other. Romeo proposes to Juliet but she's not sure. Heck, they just met a couple of hours ago. She asks if this is for real and Romeo promises it is. Juliet is to send someone to find him at 9:00 so that she knows what their elopement plans are.
And that is act two, scene two in a nutshell.