Wikipedia defines stimming as a repetitive body movement that is hypothesized to stimulate one or more senses. The term is shorthand for self-stimulation. Repetitive movement, or stereotypy, is often referred to as stimming under the hypothesis that it has a function related to sensory input. This would include such things as: rocking back and forth, knee bobbing, spinning toys, flapping of the hands or arms, making funny noises, facial tics, certain types of singing or talking, nail biting and many other examples.
Now why do Aspies do this? The function of stimming and how it is designed is to provide nervous system arousal. The theory being that it helps autistic people "normalize". I'm not sure about the "normalizing" part. But it does help us to relax. I have read a few other blog posts about this subject and I agree with most of what they say. It allows an Aspie to focus on sensitivity and relax the thinking parts of the brain. And the ability to stop thinking, even for a short while, is a relief.
As embarrassing as it may be for myself, I wish to share what exactly I do. I'm only sharing this because I want people to be aware of such things and to help anybody with Asperger's. I have a tendency of flapping my hands when I am overstimulated. When I am nervous or bored I rub my fingers along my palm. I make odd repetitive noises sometimes. People have seen me do some of these things and it is very embarrassing. But it cannot be helped. It's an Aspie thing. It's what we do.