Why Go Vector?
You can resize without picture loss. A good one for those cartoony type sites.
How Do you Do it?
Despite all of the naysayers who may tell you that Photoshop is NOT a Vector program (they may recommend something like Illustrator), the reality is that Photoshop - when used correctly - can negate all of the naysayers.
Vectors are simply the types of graphics that can be resized without losing any image quality. Newer versions of PS offer this ability, somewhat, allowing for greater control of your images, as well as the ability to draw illustrations for use with Flash animation, comic strips, or brochures.