I have been hearing the term vector images lately. Whact exactly is vector. I know this may seem like a silly, please be nice
Vector is a format which can be used for very large purpose. If you stretch vector format as big as a mountain, the image from vector format is still clear. But if you enlarge pixel based vector like jpg, bmp, etc, the image would be looks horrible
since abudz didn't really answer the question. Raster images use pixels to make a picture. Every little square is a different color that makes up the whole image. Vector images use mathematical equations to decide how the picture should look, allowing for unlimited scaling/quicker editing. Vector graphics are great for logos and things that you will need to reproduce in different sizes/colors/etc.
Adding to what JahRasta311 said, Raster images is made from each pixel being a set colour. When you zoom in the image becomes blurry and pixelated. Vector images will always appear crisp and clean as mathematical equations are used to define all of the lines, shapes and colours.
basically pixels are made up of squares and vectors are smooth very sexy stuff. each has it's own purpose.