The wheel system is designed to provide an API to the Master, which is accessible via programs that give external access to the Master, such as Salt API.
One of the first things that you'll find when writing wheel modules is that there is no command-line program available for testing wheel modules directly. Wheel modules generally include functionality that would be available via some other means, were you logged directly in to the Master, but are still useful when manual access is not an option.
For instance, possibly the most commonly used wheel module is key, which allows a programmatic way to manage Minion keys without using the key command. Because wheel modules are available to the reactor system, you can write reactor modules that can automatically accept or delete keys for Minions based on predefined conditions.