Jessica,
That may be a simple question, but it begs for an incredibly involved answer!
In short, Quickstep is sort of a faster version of Foxtrot. The music is usually some sort of Jazz or Swing-type 4/4 with a tempo range of about 50-52 measures per minute (200-208 bpm). Common examples of Quicksteps are Sing Sing Sing by Benny Goodman, Billy-a-Dick from the soundtrack to "For The Boys", and Let's Face the Music and Dance sung by Vic Damone or Nat King Cole. If you would like to hear some samples of Quickstep music, drop by the Ballroomdancers.com music section at www.ballroomdancers.com/Music.
Quickstep is a traveling dance which moves quickly around the line of dance. Basic movements are made up mostly of chasses and lock steps, with or without turn to the left or right. Steps are counted in various combinations of slows and quicks. The character of movement is light and springy, reflecting the bright, upbeat flavor of the music.
I hope this helps a little bit. I welcome others to add their 2c as well. If you have more specific questions, please feel free to ask and we'll be glad to help.
Sincerely,
Jonathan Atkinson