From the documentation, I'm seeing that it is a simple weighted average of the group utilities and the weights being the probability of group membership (https://www.sawtoothsoftware.com/help/lighthouse-studio/manual/index.html?hid_smrt_useslatent.html
However, generally we would recommend to use HB to produce individual-level utilities. This allows respondents to be unique, rather than be constrained to a weighted average of the groups.
I think the main use of average probability membership is one part of evaluating cluster solutions if you are trying to pick between, say, a 3 group versus a 4 group solution. Higher probability on average would indicate a "stronger" cluster solution, and would be used alongside other things like how many people are in each cluster, etc. to help you choose with N-group solution to move forward with.