3e had two aspects to it that made melee fights devolve into "stand next to the other guy and wail on each other until one is dead".
1. Full attacks. If you wanted to make all of your attacks, you couldn't move more than 5 ft in a round. Moving more would take a move action, which meant you could only make a standard (single) attack.
2. Attacks of opportunity. If you moved out of a square within an opponent's reach without taking precautions, they'd get a free attack.
In 5e, #1 is completely gone, and #2 is significantly reduced – now you only take an opportunity attack if you try to leave someone's reach entirely. As long as you stay inside their reach, you can run rings around them. That means that in order for a tankier character to protect a more fragile one, they have to stay some distance away from them, or the bad guys can just move past them.