Vibrato is a slight oscillation or, put more simply, wobble in pitch. A good way to visualise it is to think of the left hand of a violinist, which moves rapidly in order to produce this sound:
Why is it used?
It is way of adding expressivity to music. In some circumstances a note played 'straight' can sound too cold. We use vibrato to produce a warmer, more emotional sound.
How do I play with vibrato?
There are three ways of achieving a vibrato sound on the trumpet:
1. Finger vibrato
This method is a little similar to violin vibrato, it being activated by the fingers in contact with the instrument. With the right hand the trumpeter exerts a small amount of downward force, at the same time rocking the hand forwards and backwards. A very obvious example of this can be found in the trumpet playing of jazz great Louis Armstrong. Notice how on some of the longer notes his right hand moves backwards and forwards on the valves to create a fast vibrato sound:
It is also possible, however, to produce much more subtle effects using hand vibrato, as Barbara Hull explains in this excellent introduction to the technique:
Tip: When using finger vibrato be careful not to move the instrument too much. On the one hand too much movement can interference with your embouchure, sometimes dangerously so; on the other it has the potential to sound not like vibrato, but that you are nervous.
2. Jaw vibrato
Perhaps the most commonly used method, here vibrato is produced by the movement of jaw, lips and tongue. Practise by blowing through the instrument with a straight 'too' sound. This establishes your central pitch. Now try to bend the pitch slowly downwards by changing the to a 'you' sound. Once you feel confident you can start to speeds this up to produce a true jaw vibrato, as Reggie Smith explains, here:
3. Diaphragm vibrato
This is also sometimes referred to as 'flute' vibrato, being the most common method of producing vibrato on that instrument. As the name suggests, it is produced by altering the flow of air from the diaphragm. Instead of releasing the air with one long 'haaaa' sound, it is released as a 'ha ha ha' sound.
It is fair to say that this is probably the least commonly used vibrato on the trumpet, with many saying that it produces less pleasing results and, especially, has the additional danger of weakening the airflow. Nevertheless, some great players, such as Roger Voisin (Boston Symphony Orchestra 1935-1973), have used it.
You should probably, however, concentrate on learning the first two methods.
When should I use it?
Even harder than learning how to produce a good vibrato is knowing when to use it properly. Here are a few tips, however:
Unlike a string section, where all of the individual players vibrato at the same time, you will probably not use this type of vibrato when playing in larger ensembles. There will always be contexts where the opposite is true, but in this situation, if in doubt, don't.
Conversely smaller ensembles, where there is more of a solo element will allow you to use vibrato more freely.
Solos. Go for it! The mark of a truly great soloist is in his or her use of a beautiful vibrato.
Performance practice. Some repertoire traditional demands a different approach to vibrato. Baroque music, for example, will use vibrato rather sparingly. If you are playing jazz or Mariachi music, however, the vibrato will be often and wide.
The musical mood. Quiet and/or expressive music is often especially suited to vibrato. Loud and majestic music can sometimes sound coarse if there is too much vibrato.
Personal style and sensibility. This is where we truly get into the artistic part of trumpet playing. The truth is, in any given situation there is often no exact rule as to how wide or fast your vibrato should be or whether you should use it all. You must decide. The only way to truly master vibrato is through experience and through listening to many great players.