Let us take an example to understand how the force Branch Permission works
Consider the Force Branch Work Item Permission checkbox is checked
Now suppose you create a work item TASK in V1.0 and then you open the TASK to Edit in Advance version say V2.0
Then By default Branch checkbox would appear checked and user cannot uncheck the branch checkbox. Means the user is forced to branch the work item on update in Advance Version
Consider the Force Branch Work Item Permission checkbox is unchecked
Now suppose you create a work item TASK in V1.0 and then you open the TASK to Edit in Advance version say V2.0
Then user has an option to check /uncheck the Branch checkbox during update of work item.