Hit Points
The concept of hit points has not changed in the new edition. Nor has the fact that a character gets new hit points at every level beyond 10th. That was a great change that was made from 2nd to 3rd edition.
The way in which a character gains hit points has changed. Since the beginning, a character has rolled a die to determine the number of hit points gained. This die was determined by character class and modified by Constitution.
Now, a character's hit points are not determined by a die. The character gets hit points based on a set number (12 for example) and adds a modifier based on Constitution. This means less variety in the amount of hit points characters can have. It also means less variety in characters since whenever you make something set instead of random you cut down on the variation.
This is yet another break for decades of tradition. Also, in this case, I think it is not a change for the best or one that is irrelevant. It is a change for the worse.