What happens
Romeo, having slipped away from his friends, climbs the wall into the Capulet orchard. Juliet appears at her window, alone, thinking aloud about Romeo and wishing he were not a Montague. Romeo, hearing her, speaks. They confess their feelings. Juliet — practical and quick — proposes that if Romeo's intentions are honourable, he should arrange a marriage and send word the next day. The Nurse calls from inside. They part, twice; reunite, twice; finally agree to send word by nine o'clock the next morning.
Why it matters
This is the most rewritten scene in literature, and it's almost entirely composed of Juliet doing the work. Romeo is at his most florid — "It is the east, and Juliet is the sun" — but Juliet keeps the conversation tethered. She's the one who interrupts him when he tries to swear by the moon ("O, swear not by the moon, the inconstant moon"). She's the one who flags that the love is "too rash, too unadvised, too sudden." She's the one who proposes marriage. The scene looks romantic; it's mostly Juliet doing logistics.
Shakespeare also uses this scene to introduce the play's argument about names. "What's in a name?" is a teenager doing philosophy in a garden. The play, three acts later, will answer her: rather a lot, actually. But the scene takes her wish seriously enough that the whole tragedy can read as the world refusing to grant it. Juliet's "deny thy father and refuse thy name" is precisely what no one in Verona can do.
Dramatically, Shakespeare writes the scene's pacing as a series of partings. Three times Juliet says goodnight. Three times she comes back. "Parting is such sweet sorrow" is a line you've heard in greeting cards — it's also a piece of stage business about not being able to leave. The play is already practising the rhythm of the rest of it: two people who keep almost-leaving each other, never quite, until they have to.