A third party developer is a company that makes
video games and then publishes them for any hardware platform it would like to, provided the parent company of said platform will allow it (i.e.
Squaresoft may want to make
Gameboy Advance titles, but
Nintendo won't let them unless they make
GameCube titles as well.) There are usually several different development teams within the company, each working on seperate products.
Examples of this would be
Capcom,
Konami and
Electronic Arts.
For information on
first party developers and
second party developers, click the links.