The term case duration is used in the business world. It explains the amount of time from when the case was opened to when it was closed. However, it is usually based on hours and not years. Salesforce is one place where case durations are seen and calculated. In many cases, people want to get paid for the hours that they put into a project.
One way to do this is through the case duration. It would take a count of the number of hours this case was held open. Of course, the person will have to add in the times when they worked on the case. This function is only used to determine how many hours long the case was held open until it was closed by someone.