Vibrato is a technique used to add expression to sustained notes when playing guitar. With it the player achieves a fluctuation in pitch, using slight bendings back and forth, though there are more advanced types of vibrato which apply the pressure parallel to the string to achieve a similar effect (Classical vibrato).
Vibrato can also be achieved with your guitar, provided it has a whammy bar.
Related GMC Lessons
There are dozens (even hundreds!) of lessons regarding vibrato at GMC. These are just a few that you might find useful: