Tokens are small bits of text that can be placed into larger documents via simple placeholders, like %site-name or [user]. The Token module provides a central API for modules to use these tokens, and expose their own token values.
Note that Token module doesn't provide any visible functions to the user on its own, it just provides token handling services for other modules.
For Drupal 6, the Token module provides a "Token Actions" module which can be enabled separately. This provides several "actions" for the Drupal core Actions/Trigger modules to use that take advantage of the Token replacement functionality.
Modules that use the Token module and provide tokens via the API include Organic Groups, Pathauto, Comment Notify, and Commerce. Also check out the full list of modules that use or provide tokens or the list of open issues tagged with 'token'.
#D7CX: The basic token API is now a part of Drupal 7! Unfortunately, other things like the a browsable token UI, and field & profile tokens did not make it into core and will be supported here for Drupal 7.