How did the Cavs win 66 games and look so dominant during the season?
They beat up on weaker teams but when they have to go against good teams they falter. Their regular season record against the best teams in the league should have been a strong indicator that this would happen.
Their regular season record against the Lakers, the Celtics, and the Magic was not spectacular. The Magic historically have done very well against them, and the Lakers were the one team to beat them in a meaningful game on their home court.
The Cavs simply don't have what it takes to beat a real contender in a 7 games series. Until they get more true All-Star caliber talent than just LeBron, they aren't going to be any better.
The fact that they are fantastically coddled by the league with the amount of free throws LeBron gets and the fact that he never gets in foul trouble also means they don't have to face a whole lot of adversity during the course of the season, meaning they aren't really prepared for tough series like this one.
That's how the Cavs can win 66 games and sweep through the first two rounds and then get dominated by a true contending team that is built to win playoff series (e.g. a team not based around one player).