Vector vs. Raster
Long story short: VECTOR is for text and logos, RASTER is for photos.
In printing, everything that we digitally produce falls into 2 categories, VECTOR and RASTER formats. Both are important, but there are cases when one serves us better than the other. There are even cases when only one of these formats will do. A photo will most likely be RASTER and a logo will most likely be VECTOR. Keep in mind that for making dies and for many of the advertising specialties that we offer, only VECTOR is acceptable. RASTER cannot be used for these processes.
VECTOR is created using lines and coordinates, where RASTER is created by many pixels making up the image. In the example above, we exaggerated the pixels in the word RASTER, so you can see that it is made up of a bunch of squares. VECTOR graphics will have smooth lines at any enlargement. RASTER graphics can always be reduced, but they lose quality when they are enlarged.
Low-resolution vs. High resolution is another post altogether.