Why are crystals bigger when liquid rock cools slowly?

Crystals being cooled rapidly means a very high temperature gradient. When the temperature gradient is very high the number of nucleation sights is very high.(To visualize, think of cold water being poured into a very hot pan--it forms a large number of bubbles). Thus crystallization starts at many such nucleation sites and we have smaller crystals as the overall volume is constant.

But when the temperature gradient is not high, there aint enough nucleation sights and solidification (nucleation) occurs at far fewer sites. Thus assuming constant total volume in either case, the crystals are smaller.