What can be said about an igneous rock with larger crystals compared to one with smaller crystals?
It has had more time to crystallise
Intrusive igneous rocks are as you described, magma that sits deep in the crust and slowly crystallises.
The main control on crystal growth is time, if a lava is erupted onto the Earth's surface then it has little time to crystallise and therefore the grains are smaller. This could be something like a basalt (which is an extrusive igneous rock):
But if you leave the magma in the crust and give it time to crystallise, then the grains will be much bigger like that of a granite: