Like all brass instruments, the sound of the trombone is produced by the players buzzing lips, which cause the air inside the instrument to vibrate. The pitch of the instrument is changed by a combination of a telescopic slide, and the players embouchure (the shape made by the mouth) buzzing at different frequencies, causing the instrument to move up or down the harmonic series. Its actually much simpler than it sounds!
The bore or width of the tubing usually increases in size after the slide section, and gradually flares into the bell of the instrument - the way each trombone varies in this respect gives it its individual character. Its also crucial to the tuning of the trombone that this aspect is designed correctly - budget models may not have had the time spent on them to ensure the instrument responds as it should!