A theme can optionally use a functions file, which resides in the theme subdirectory and is named functions.php. This file basically acts like a plugin, and if it is present in the theme you are using, it is automatically loaded during WordPress initialization (both for admin pages and external pages). Suggested uses for this file:
- Enable Theme Features such as Sidebars, Navigation Menus, Post Thumbnails, Post Formats, Custom Headers, Custom Backgrounds and others.
- Define functions used in several template files of your theme.
- Set up an options menu, giving site owners options for colors, styles, and other aspects of your theme.
The default WordPress theme contains a functions.php file that defines many of these features, so you might want to use it as a model. Since functions.php basically functions as a plugin, the Function_Reference list is the best place to go for more information on what you can do with this file.