Vibrato can be described as a slight fluctuation in pitch or tone intensity to enrich the sound.
Vibrato is very much an advanced technique in saxophone playing.
It should not be attempted until the embouchure is well and truly settled.
I recommend you complete at least 3 years of regular saxophone practice before you commence vibrato exercises.
When to apply vibrato depends very much on the type and style of music you play and also relies heavily on personal musical taste.
In Jazz and Popular music a long note is typically started 'straight', with the vibrato coming during the second half of its duration. The vibration amplitude usually diminishes towards the end of the note.
Vibration frequency of the vibrato varies, but generally lies within the range of 250 to 280 waves per minute.
When playing vibrato in a group make sure that your frequency matches that of your section leader (or of the rest of the group).
(Down - Up - Top)
SAX 10.2 - The Jaw Vibrato