The word vibrato comes from the latin ‘vibrare’ meaning ‘to shake’ and it is a slight (and often rapid) wavering of the pitch for emotional effect. Many singers, whether classically trained or not naturally have a vibrato to their voices and in terms of string playing this is often an ever present feature of music making.
For music of the 16th and 17th century, only a small and refined vibrato is occasionally used (if that!). The phrasing and expression generally comes from the bowing rather than the motion of the finger on the string, although in 1751, the famous Italian violinist Geminiani advised vibrato to be used ‘as often as possible’ and there is documentary evidence to support the use of vibrato for music of this period.
When a composer or string arranger specifically wants a passage to be played without vibrato at all, the direction ‘senza vibrato’ would be written in the score. Particularly when combined with a Sul Tasto sound, the use of no vibrato can be very effective when applied to the entire string section in giving a very ‘pure’ and gentle, velvety feel to the sound.
On the other hand, adding a lot of vibrato tends to make the pitches sound less pure and for some reason, thickens up the entire sonority of the strings. This could also be indicated by a composer or arranger by the direction ‘molto vibrato’ and gives a very romantic expression to the strings, particularly effective when played loudly. The music could start softly without vibrato and build up in intensity as the vibrato increases.