V-brakes (a.k.a. side-pull cantilever) are cantilever brakes.
They were developed for mtbs, for two main reasons: power (the mechanical advantage of the longer arms/cable pull) and the need for a brake to work well with suspension.
Traditional cantis rely on (centred) cable stops mounted somewhere on the frame; these don't play well with the movement of suspension (front and/or rear), or with the sometimes complex cable routing required for rear suspension. Solution: develop a brake that does away with the centred cable stops.
Once discs became mainstream, v-brakes began to disappear from mtbs, but have remained common on hybrids and touring bikes (power, relative to traditional cantis).