Many plants have just one stem emerging from the ground and can not be propagated using this technique. However, there are quite a few different plants that have multiple stems emerging from the ground and can be propagated through division. A few examples would be Hostas, Mums, Ornamental Grasses, and many perennial flowers.
Division is exactly as it sounds.
You just dig up the parent plant that you intend to reproduce and quite simply divide it into many plants. Of course the size of the parent plant will determine how many times you can divide it. If you don't care to reduce the size of the parent plant, then you would only remove a few divisions from around the edge of the parent plant. You can probably do so without actually removing the parent plant from the ground. Just scrape the ground clean around the plant so you can see exactly which sections of the parent plant you would like to remove, take a spade and force it into the ground between the parent plant and the division you are removing.