The user in the system represents the person who is using the CRM system. The user can be you or any of your staff who have access to the system.
For example, the entire marketing team in your company has access to the system. They can view profiles of the prospects and plan activity from the system. Thus, that makes them the user of the system.
On the other hand, contacts are the lists of numbers and pieces of information about your existing customers, prospects, and also your vendors.