Raster and vector are two forms of digital graphics.
Vector graphics are illustrations created using design software (such as Adobe Illustrator) and can be scaled larger without any loss of quality. Vector graphics are assigned a mathematical expression that the design program reads and uses to create the visual form of the shape. This means when you scale the vector graphic, the program simply re-draws it larger, so the shape is preserved at the highest quality.
Photographs as well as most graphics and images found on the internet are raster images (pixel-based). Increasing the size of raster images will result in a poorer quality and blurriness. This is because a raster image is made up of pixels, which are smaller units each with their own colour information that together form the image. Pixels are very small and are unnoticeable in a high quality image viewed at 100%. If you scale the image larger however, the pixels will also be made larger and will therefore be more visible. Being able to see the individual units the image is made of is what is referred to as "pixelation" - this makes the image appear to be fuzzy or of poor quality.
Below is a table that shows which file formats support vector and raster:
Photoshop now supports vector-modeled-graphics; but exports them as raster in most cases.