When you block somebody, a couple of things should happen.
Firstly, you will receive no communications from them.
Secondly, during any transition where matchmaking is at work (so basically, hyperspace jumps, entering and exiting super cruise) you are much less likely to be matched with the blocked Commander.
Blocking becomes weaker when it comes up against friends (and next year, player wings), because if a blocked Commander is in the same session as a friend (say, because they haven't blocked the Commander, the blocking effect is overruled by the friendship matchmaking.