Fonts have various styles and qualities. Let’s start with the basics of the serif condition:
Serif Fonts are basically characterized by the flared extensions, or strokes, on the tips of letters.
Sans Serif Fonts are the ones that do not use that extensions. They have plain endings, and appear blockier than serif fonts. (“Sans” means without, and “serif” refers to the extra strokes, or lines.)
Cursive Fonts resemble hand-written pen or brush strokes, often have artistic ornamentation, and sometimes have strokes that connect the letters together.
Monospace Fonts get their name from the fact that each letter takes up the same width of space.
Fantasy Fonts are primarily decorative, and are not designed to be used as the main font for long passages of text.
Fonts are designed and used according to the context they belong to. For example, Gothic writings were popular in the Western Europe till 17th century which is an intimidating font style that was used in highly sophisticated literature and religious texts. It was called Gothic by the Renaissance Humanists because they thought it looked barbaric.
Nowadays, sans serif fonts are used more frequently because they are more legible and mostly useful for web and graphic design.
Here are some interesting typography I digged out: