Vocal vibrato is the regular, consistent pulsating of pitch through variations in the larynx.
We use vibrato in singing in many ways, depending on the style of the song we are singing. There is much argument among experts about historically-accurate use of vibrato. Currently, early music (Baroque era 1600-1750) is thought to have been sung with straight tone (little or no vibrato) with vibrato used as an ornament to color certain notes or text. Vocal music in the Classical era (1730-1820) is thought to have been much the same, and into the Romantic era (1830-1900) it is thought that vibrato in operatic literature was used more or less consistently. So we have the sense that more "classical" styles of vocal music usually indicate the presence of more vibrato, and we expect to hear it in operatic voices. Contemporary styles of vocal music (pop, jazz, musical theatre, folk) use varying degrees of vibrato, depending on the individual voice. You will hear voices that have consistent vibrato, and others that use it to color certain notes. Studies show that in general, people enjoy a vibrato that is approximately 6 to 8 oscillations per second - if it's any slower or faster than that, it could become a too-prominent element of the sound.
Some people produce a natural vibrato without thinking about it. Others who have a more straight tone can learn to add vibrato to their sound. The presence of vibrato in the voice can indicate relaxation in the larynx, which allows the vibrations to occur. So absence of vibrato can often (not always) indicate some degree of tension in the larynx.
Find out more about vibrato at the links below, and talk to me in your lessons if you have any questions!