CrossOver monitors the installer program it launches. Some installers launch other programs to perform part of their installation, so CrossOver monitors them too. CrossOver only considers an installation to have completed when all of those programs have exited. This heuristic fails sometimes because the installer launches the newly-installed program at its completion. A common example of this is Steam. The Steam installer launches Steam when it completes. Furthermore, it can be hard for a user to properly exit Steam, because closing the Steam window just sends Steam to live in the system tray, which isn't visible by default on the Mac.
Also, sometimes installer programs hang.
Anyway, the Force Installer Completion button is a way to tell CrossOver to stop waiting for the programs to exit. Instead, it should just proceed as if they had exited and move on to the next step in CrossOver software insallation process, like scanning for new Windows Start Menu shortcut entries and translating those into Mac launcher applications.
I hope that answers your question.