Great question! Static electricity is one of two types of electricity. The other kind, where electricity is flowing, is the one you are probably more familiar with. This kind is used all around your house in things like lights, televisions, the computer you are reading this on, etc. When we talk about electricity, we say that there are two kinds of charges, positive and negative. The important thing to remember about charges is that opposite charges attract each other and like charges repel each other. E.g. positive attracts negative, and negative repels negative.
The word "static" means that something is sitting still and not moving. So static electricity deals with charges that do not move. (The electricity used in lights, TVs, etc is made up of moving charges.) Basically static electricity means how charged up something is; how many charges of one type or the other are in a certain object. One example of static electricity that you are probably very familiar with is when you walk across a furry carpet and then shock yourself when you touch something like a metal desk, a person, etc. When you walk across the carpet, you build up static electricity, i.e. you create an imbalance of charge in yourself so that you are either more positively charged or more negatively charged. That means that you have an excess number of one type of charge that want to get away from each other (because like charges repel). When you zap the door knob or your friend or something else, the charges in you that want to get away from each other move through your finger into the thing that you are touching.
A more dramatic example of static electricity is the Van de Graaff Generator. I won't get into the details here about how it works, but it basically separates positive and negative charges. When enough charge builds up, it will make a zap, kind of like when you walk across a carpet and zap something by touching it, but the spark that the Van de Graaff is a lot bigger and easier to see...
Hope that answers your question!
(republished on 08/02/06)