The two main use cases are for sunsetting applications and keeping data when you don't want to pay the full licensing costs for the application. For example, for archival purposes, you may need to keep all that data where you have three accounting systems in your sunsetting from mergers and acquisitions. You can move this data into InfoArchive.
Another use case is moving data out of large systems to make them manageable. So, if you have a large Oracle SAP implementation, you can move all the data from a certain period out of that system. It is still online and accessible for reporting and moving into InfoArchive.