(2) In DOS and some other operating systems, one or several letters at the end of a filename. Filename extensions usually follow a period (dot) and indicate the type of information stored in the file. For example, in the filename EDIT.COM, the extension is COM, which indicates that the file is a command file. (Depending on the operating system, the punctuation separating the extension from the rest of the filename may or may not be considered part of the extension itself.)

Also see Data Formats and Their File Extensions in the Quick Reference section of Webopedia.

(3) In Macintosh environments, a program that extends the system's capabilities. When they reside in the Extensions folder, extensions are loaded into memory when the system starts. On older Macs (System 6 and earlier), extensions were called inits.

(4) Same as plug-in.

Wotsit's Format 
Programmer's resource for detailed file format and data format information.

Data Formats and Their File Extensions
Extensive alphabetical list of file extensions, with the applications that create them.