Division is a process of plant propagation where a vigorous specimen exhibiting many stems is dug up and separated into several sections, each with a few stems, and, most importantly, a viable root clump, which are then replanted.
Many perennial ornamentals benefit from this process, for if they are growing well, the new stems each year eventually start to crowd each other out for space above the ground and nutrients below it. Division will result in several healthy specimens, each growing in newly prepared soil. People will often give away some of these divisions to friends, if there are more than they can use themselves.
In the case of some highly hybridized cultivars, division is the only method of reproduction available, since the plant, while having been selected for attractive flowers or food or fiber production, will have lost the ability to successfully set viable seed.