From Mini-blockchain Project
The inversion database contains instructions for reversing changes made to the account tree. The transactions alone are not enough to tell you exactly how to reverse changes made to the account tree because some information is lost in the process. For example when the withdrawal limit is updated the old withdrawal limit cannot be recovered unless you record what is was, and that's why we need inversions. One reason we might need to undo changes to the account tree is to handle blockchain reorganization events where nodes need to switch chains by unwinding and fast forwarding.