The average fan has known about his incredible athleticism and strength for a while. That was common knowledge after he put on the Superman cape and won the dunk contest. But now the average fan can realize how Dwight is a skilled player. They can see what all his work he has put into his game. Those nice post moves and footwork need to be ready to go if Dwight wants that recognition.
He also can be recognized in the upper tier of young players. Everytime you hear David Stern do a TV interview during a game, he names certain players that are making his league better. Dwight has to perform to the best of his abilities on both ends during this series; then, David will get his name right near the top of that list.
I'm sure being well regarded by the general public is no big deal for Dwight. He knows how good he is. But, the Finals can help him be classified where he should be. He should be known as a guy that is a great overall player, not just an incredible athelete.
All it really comes down to is having fun and playing basketball (as Dwight has told the media it's all about). That will cement you as a top center in the league, Dwight. People may not go as far as the best in the league yet, but your time will come, young fella!