Modules are simply an addition to the Cascading Filesystem. A module can add any kind of file (controllers, views, classes, config files, etc.) to the filesystem available to Kohana (via Kohana::find_file). This is useful to make any part of your application more transportable or shareable between different apps. For example, creating a new modeling system, a search engine, a css/js manager, etc.
Kolanos has created kohana-universe, a fairly comprehensive list of modules that are available on Github. To get your module listed there, send him a message via Github.
Mon Geslani created a very nice site that allows you to sort Github modules by activity, watchers, forks, etc. It seems to not be as comprehensive as kohana-universe.
Andrew Hutchings has created kohana-modules which is similar to the above sites.
Modules are enabled by calling Kohana::modules and passing an array of 'name' => 'path'. The name isn't important, but the path obviously is. A module's path does not have to be in MODPATH, but usually is. You can only call Kohana::modules once.
Kohana::modules([
'auth' => MODPATH . 'auth', // Basic authentication
'cache' => MODPATH . 'cache', // Caching with multiple backends
'codebench' => MODPATH . 'codebench', // Benchmarking tool
'database' => MODPATH . 'database', // Database access
'image' => MODPATH . 'image', // Image manipulation
'orm' => MODPATH . 'orm', // Object Relationship Mapping
'oauth' => MODPATH . 'oauth', // OAuth authentication
'pagination' => MODPATH . 'pagination', // Paging of results
'unittest' => MODPATH . 'unittest', // Unit testing
'userguide' => MODPATH . 'userguide', // User guide and API documentation
]);
When a module is activated, if an init.php file exists in that module's directory, it is included. This is the ideal place to have a module include routes or other initialization necessary for the module to function. The Userguide and Codebench modules have init.php files you can look at.
A file in an enabled module is virtually the same as having that exact file in the same place in the application folder. The main difference being that it can be overwritten by a file of the same name in a higher location (a module enabled after it, or the application folder) via the Cascading Filesystem. It also provides an easy way to organize and share your code.
To create a module simply create a folder (usually in DOCROOT/modules) and place the files you want to be in the module there, and activate that module in your bootstrap. To share your module, you can upload it to Github. You can look at examples of modules made by Kohana or other users.