It's one of those perfect moments where a minor piece of Lenny's music and a minor piece of Robbins's staging united to create a breathtaking moment.
It start with Maria's last line in the dress-shop scene, "Because tonight is the real beginning of my life as a young lady of America." Robbins had her hold her dress out at the sides and start to twirl, in the classic movement of a young girl like Cinderella imagining herself at a ball, twirling and the dress billowing out.
The music is the little repetitive transition figure (DAH-da-da, DAH-da-da, DAH-da-da...), which I remember being told is based on the interval that Lenny used to unite the whole score ("Ma-ri-a!" "Some-where!" etc.), but you'd have to ask someone more musically included to explain how intervals are similar.
Maria twirls, the music builds, she is joined by four Jet and Shark girls, the set for the dress shop slides off, leaving the girls twirling in limbo as the music becomes more and more intense.
The, all of a sudden at precise moments in the build of the music, the girls twirl off, the Jets enter from Stage Right and cross left, the Sharks enter from Stage Left and cross right, the music changes to the piece that opens the gym scene (which Bernstein called "The Blues"), the streamers drop down suddenly from above, and the stage is filled with the kids dancing at the gym, dancing hip-to-hip in a sexually suggestive manner that starkly contrasts with Maria's innocence.
You can hear the build of the transition music and the build with the four Jet and Shark girls in this clip from the movie. But since Robbins and Wise were using a blurred technique for the transition, you won't see the streamers.
http://youtu.be/VC892WVJh4A The moment when the streamers came down, I believe, is at 0:34.
But I can just hear Mr. Robbins saying, "No, no! That's wrong. That's all wrong. How stupid can you be? That's the wrong moment in the music. You've got it all wrong. Do it again. Take it from Anita's exit." And the stage managers would have to roll on the dress-shop set and roll up the streamers, and everyone in the cast would have to rehearse the transition into the gym scene over and over and over and over and over again, until Jerry Robbins decided it was perfect. Or more likely, till he got tired of making it perfect.
But it was perfect.