I didn't read your answer, or any of the other responses yet, preferring not to be influenced by other posts.
It means to me, that I am solely responsible for what happens to me when I dive. It's up to me to make sure that I have the skills, the training and the equipment necessary. It's up to me to make sure that I am physically fit enough for the dive and that my equipment is maintained and in good working order. I am responsible for making my own dive plan and in executing that plan.
The social part means that I am doing all of the above with a like minded buddy who is just as capable of doing each of these things on his own. I do not dive with them beyond my abilities because I believe my buddy can keep me safe, rather I dive with him because I'm assured he wont need me to do that either. As part of the socializing, we will go over the plan together, ensure we have what we need as a team and that we understand what each of our roles is during the dive. But if things go awry, each of us if fully capable of executing any or all of the plan by ourselves.