A waveform which, as seen on an oscilliscope or in a waveform editor, rises in a straight line from a minimum value to a maximum value (or vice versa), then snaps back to the starting value. The result looks like the teeth of a saw, hence the name. Harmonic analysis of the sawtooth wave shows that it contains a significant amount of even harmonics, unlike many of the other waveforms produced by common VCOs. The audible result is a sound that somewhat resembles a saxaphone or a woodwind instrument.
Note that the terms "sawtooth wave" and "ramp wave" mean fundementally the same thing, but are used inconsistently. Whether the wave value goes up or down from the starting value makes no difference audibly (as one is merely the inverse of the other), but the two forms do of course act differently when used as a control signal. Some VCOs and LFOs output both, and some parties refer to one as the sawtooth and the other as the ramp, but there is no consistency as to which is which.