The fonts available on a browser (the User Agent in W3C speak) depend on what the user has installed. If a font is specified that doesn't exist on the UA then the default font will be used. Certain fonts are assumed to exist across all browsers, these being a monospaced font (for typewriter like display) and a ... font (for regular text).
Because a specific font might not exist on all platforms, a more general description -- the font family -- can be used. This just identifies a particular style of font.
All of these should work.
Some examples of browser specific fonts, assuming they have been installed.
A more interesting development is the delivery of both the font information and the Web Page. This allows a page to be displayed using the same font the designer used.
Netscape and Microsoft have used different approaches for this and the ultimate winner is unknown. Although Microsoft worked with Adobe and appeared to be the early leader, the Bitstream approach, initially used by Netscape but now works with Internet Explorer also, appears to have the momentum.
Examples of embedded fonts