What does it actually mean to bless a same-sex couple, and does the blessing confer anything?

Nobody really knows what it means, and I do not think the Vatican knows either, because that is part of the game: keep it ambiguous and do not define too much, so no one can point to what you have done wrong, while the real aim, preserving the definition of marriage, is quietly eroded. The stated loophole is that the blessing could be good if the couple intends to cease their misconduct, but what homosexual couple comes forward saying they are trying to end their relationship and want a blessing to help them along. Once you open the door to any such relationship, you invite trouble, because they will nitpick to the next stage; it works like a cancer that metastasizes. If a couple truly wanted to repent, the right order is to stop the sin first and then receive a blessing, not receive a blessing to continue in sin. The Church here has it backwards. So to answer directly, the blessing does not mean anything and confers nothing; if anything, those who seek it while unrepentant only seal their fate further, whatever priests like James Martin present to the contrary.