All digital images are either raster graphics or vector graphics. Different file types designate different types of graphics. Jpg ("jpeg"), gif, tiff, and png files are generally raster, while eps and ai files are vector. For a comprehensive list of file types and their characteristics, please see the wikipedia page.
Raster graphics (also called a bitmap) is a way to construct a picture using small building blocks called pixels. When enough pixels are included close together, your eye stops seeing a collection of different points and starts seeing a whole image. Digital photographs are always rasterized.
What is a Pixel?
Just as atoms are the basic units that make up all matter, pixels are the basic units that make up all raster graphics. But unlike atoms, which have smaller component parts, pixels are the smallest unit of a picture that can be controlled. In raster graphics, pixels are small, solidly-colored squares. Wikipedia page about pixels
Using photos and graphics with the right resolution for your use will prevent your material from looking pixelized. Images intended for print (not t-shirts) need to be 300 ppi, and those intended for viewing on screens should be 72 ppi.
What is PPI?
The quality of a raster graphic is determined by the number of pixels per inch (sometimes called points per inch, or ppi): more ppi is higher quality, and fewer ppi is lower quality. If raster graphics are enlarged, the number of pixels per inch goes down, and the image becomes lower quality and may appear pixelized
Vector graphics use mathematical geometric elements (points, lines, curves, circles, and polygons) to create pictures. Because vector images are simply visual representations of geometric concepts (as opposed to raster files) they can be made infinitely large or small without losing image quality.
More about vector graphics