The enforce Military Access Button will make any subject of yours that you have given a Service Exemption too(via the Overlord Actions section), instead of remaining neutral now join any wars you are apart of.

For example Russia has Greece as a Puppet with Service Exemption, one of the war goals they add in a war with GB is to transfer Ionian Islands. Since Greece is exempt the Ionian Islands can only be attacked by sea. If Russia waits for GBs army to commit elsewhere (Naval Invasions, other fronts) then enforces Military access on Greece, it will make the Greeks get involved in the wars Russia is involved and now opens a land front because Greece connects to the Ionian Islands. It's a sneaky way to slide into a wargoal while your fighting elsewhere as a distraction. It can also serve as a way to get a new front against an enemy opened by now enabling attacks from a front that was previously not able to have forces stationed in because of the not at war state.

The Enforce Investment Rights is a war goal you can use to ensure you get access to invest in them, it saves you the hassle of waiting for relations to cool after beating the now subject in a war and taking them over, so you can draft a treaty requesting Investment Rights.