There are two types, vector and raster.
All web based images are raster, however the source files for those images can be vector. Vector is the plotting of points rather than the plotting of pixels, which is what raster is.
Vector images contain mathematically plotted points so that it is endlessly resizable. Raster on the other hand uses absolute pixel points, so if you try to blow it up you will eventually see the pixels.
The vector format is most often used for things like logos because they need to be used for a variety of things. All printed material is done in vector as well.
Raster is mainly used for websites, where the quality doesn't have to be top notch and the image and file sizes are small. All of the images that make up this website are raster. Flash on the other hand is vector.