How to play saxophone. Vibrato.You know when a singer holds a note and it wobbles. Well that's vibrato.
There's two ways of acheiving this. You can use your lip or you can use your diaphragm.
Lip Method - Probably the easier of the two. Play and hold a note and then slacken and tighten your embouchre whilst playing. This should have the effect of flattening and raising the note. It's an easy enough thing to do but not so easy to do quickly and well.
Diaphragm Method - A bit trickier to do and requires good diaphragm control. Play a note and hold it. Now start using your diaphragm to force air out of your lungs in bursts. Not so easy to do but with practice you can acheive it.
The idea of vibrato is to bring a little colour and life to the note. Opera singers do it all the time.
You really have to practice getting your speed up on this for it to sound good. If you are new to playing you may well acheive the effect by accident after a long session because your jaw muscles will be tired.