Vibrato is one of those great expressive devices that the guitar is capable of. If not for this and things like portamento, pizzicato, rasgueado and other timbral effects, the guitar would be nothing more than a very limited keyboard instrument. But vibrato is a natural expressive device that guitarists share with bowed string instruments. It originates with the voice, of course, and when the guitar or the violin or cello does vibrato it is at least partly with the aim of suggesting the quality of vocal expressiveness. For this reason it is something you do primarily with melodic notes. The guitar can achieve some intriguing expressive effects by using vibrato on melodic notes combined with muffled or staccato notes in the accompaniment. Here is Segovia doing some nice vibrato in a short piece by Tárrega:
And here is some lovely, refined vibrato on violin in a piece by Eugène Ysaÿe:
There are a lot of things you can do with vibrato: it can be even or it can speed up or slow down. The width of the variation in pitch can be narrow or wide and this can change as well. Vibrato can be so individual that you can almost identify the player, just by the vibrato. Here are two guitarists with very distinctive vibratos. First, Julian Bream, who, you will notice, has a more agitated vibrato than Segovia:
And now Eric Clapton. In the first minute of this song, you will probably hear five different kinds of vibrato!