This option "Enforce the use of latest approved versions" means, the latest approved version of objects are required when using them in another objects.
For example, with this option enabled, to create a new AC (Analysis Configuration) based on a DC (Data Configuration), that DC must be approved first. Otherwise, you can't associated it with an AC.
In the use case that, I have an existing AC which is associated with a DC that has never been approved,
1. When this option "Enforce the use of latest approved versions" is unchecked, I am able to run the AC with the unapproved DC.
2. After this option is checked and change is committed, I am still able to execute the AC with the unapproved DC.
3. But if I detach the DC from the AC, and try to re-attach the DC to the AC, it will pop up a message that the DC does not have the Latest Approved version.
You would need to first approve the DC and then you will be able to associate the DC to the AC.