This filter allows you to extend the map_meta_cap() function. This function is called by WP_User->has_cap() to convert a meta capability to one or more primitive capabilities.
For example, you want to know whether the current user should be allowed to edit the current post, the edit_post meta capability. This depends on some factors: is the user the author of the post? Is the post already published? Is the post marked as private? The primitive capabilities are edit_posts, edit_published_posts, edit_others_posts and edit_private_posts: you can assign these to user roles. map_meta_cap() checks the author and status of the post and returns the correct set of primitive capabilities this user must have to allow editing of the post (if the post is written by someone else and published, it would return array('edit_others_posts', 'edit_published_posts'), so the user must have both capabilities to continue).
Adding this idea of meta capabilities and primitive capabilities allows you to keep the base WP_User class free from knowledge of posts and post statuses and whatever, and just focus on capabilities. The actual conversion is in an external function, map_meta_cap().
The filter map_meta_cap allows you to extend the functionality, for example when using custom posts. I believe basic support is provided if you set the capabilities argument of register_post_type, but the mentioned article by Justin Tadlock and Prospress plugin provide complete examples of this. But you can customize it to completely turn the capabilities system over, if you desire.