The point of making a starter is to prepare the yeast to tackle the job of fermenting the sugars in the wort.
A stir plate is not necessary, but, then, neither is making a starter. You can make decent beer just tossing dry yeast on top of your cooled wort. Beer was made for thousands of years before anyone even knew yeast existed! However, it's easier to make great beer by doing the best that you can by your ingredients and your "wee beasties".
Yeast grow aerobicaly and anaerobicaly, meaning with and without oxygen. In making a starter, you're trying to build up the population of healthy yeast cells that are ready to go the minute they hit your wort. During the starter phase, the yeast cells have a chance to build up their cell walls needed to cover the "daughter" cells. This growth is the aerobic phase and requires oxygen. This is where the stir plate comes in.
The sitr plate keeps the yeast suspended in the starter wort, but, more importantly, sucks air into the liquid and keeps the oxygen level up.
Starters can be made without a stir plate. You just need to agitate the flask fairly often to dissolve more oxygen into the liquid. The sitr plate makes it much easier and much more convenient.