The module provides an API and a user interface for storing and reusing credit card data on subsequent orders within Drupal Commerce.

The module does not retain full card numbers locally but instead stores the remote ID of the full card data from the payment gateway used to validate and process your credit card transactions.

For the Commerce Card on File module to work, you'll need an attached payment method that implements the CIM API.
In this screencast, I'm using the Commerce Authorize.net payment method to provide Card on File payment support.