MLB experimented with clocks in spring training, then the league decided to use them in the regular season.
I don't remember the exact rules, and am too lazy to look them up. There is a clock between innings and on pitching changes. 2:30 from the last out to the first pitch, or the umpire can start calling balls, same on a pitching change so the new guy needs to jog in if he wants all his warm up pitches. I don't know if a pitcher coming in because of an injury still gets all the time he needs, probably that part of the rule didn't change. They've also limited the number of times there can be meetings on the mound. There was always a rule about how many times a coach can come onto the field each inning, but I think they are cutting down on the pitcher catcher discussions.
The instant replays can be requested directly from the dugout, there doesn't have to be a walk from the dugout to the umpire by the manager anymore.
Batters are supposed to stay in the box between pitches. They were always permitted to leave, and the umpire was always allowed to use his discretion in the past whether or not to warn the batter about excessive delays and start calling strikes. The rule was rarely enforced. This year the batter is subject to fines for leaving the box, and umpires have been told to emphasis those rules this season. Pitchers are supposed to be on a clock now, too, between pitches.
It's an attempt to speed up the game but I haven't noticed a difference. Maybe fewer batters are stepping back and adjusting gloves, cups, and helmets between each pitch, but it isn't noticeable and I don't know if it's made any difference at all.