Typography is fast becoming a dying art. Most people recognize the visual and aesthetic impact of a typeface, but few can verbalize why one works in a particular publication, or why others do not.
At large, typefaces (commonly known outside of the trade as "fonts") are divided into "serif" and "non serif". The first are characterized by little marks, or feet, at the end of lines. An example is Times New Roman. The overall feeling of these typefaces is of classic style and seriousness.
The latter are recognizable for having simple lines, and lacking the ending "feet", like Helvetica. Generally these are considered more modern and versatile.
I recommend going through the various categories of fonts in the website Dafont.com, which is an open source channel to browse and download fonts for personal use. This way you can familiarize yourself with the lingo of typography.