Firstly, there are fixed width fonts, and variable width fonts. The fixed width fonts look like typewriter text, because each character is the same width. This quality is desirable for something like a text editor or a computer console, but not desirable for the body text of a long document. The other class is variable width. The most well known fixed width font is courier.
Serifs are little hooks on the ends of characters.
For example, the letter i in a font such as Times Roman has serifs protruding from the base of the i and the head of the i. Serif fonts are usually considered more readable than fonts without serifs. There are many different types of serif fonts. Sans serif fonts do not have these little hooks, so they have a starker appearance. One usually does not write a long book using a sans serif font for the body text. Another application that sans serif fonts have is as display fonts on computer screens, especially at small sizes.