I often have to remind students to use vibrato sparingly and intentionally. Depending on their age I have various ways of communicating this. Recently I saw the following on Facebook:
Vibrato on every note is like putting ketchup all over the music.
I tried that on a young student yesterday but then his dad informed me that the student puts ketchup on EVERYthing.
But then someone pointed me to these excerpts from Leopold Auer's classic book on violin teaching:
The purpose of the vibrato, the wavering effect of tone secured by rapid oscillation of a finger on the string which it stops, is to lend more expressive quality to a musical phrase, and even to a single note of a phrase. Like the portamento, the vibrato is primarily a means used to heighten effect, to embellish and beautify a singing passageor tone. Unfortunately, both singers and players of string instruments frequently abuse this effect just as they do the portamento, and by doing so they have called into being a plague of the most inartistic nature, one to which ninety out of every hundred vocal and instrumental soloists fall victim.
Some of the performers who habitually make use of the vibrato are under the impression that they are making their playing more effective, and some of them find the vibrato a very convenient device for hiding bad intonation or bad tone production. But such an artifice is worse than useless. That student is wise who listens intelligently to his own playing, admits to himself that his intonation or tone production is bad, and then undertakes to improve it. Resorting to the vibrato in an ostrich-like endeavour to conceal bad tone production and intonation from oneself and from others not only halts progress in the improvement of one's fault, but is out and out dishonest artistically.