It's a great question and I've seen it come up in a few threads, so maybe I can help explain the thinking a bit.

MMR is an internal measure of skill used by the matchmaking system to ensure we’re placing players with, and against, players of similar skill. It’s a long-term measurement that is continually refined as you play games. In the grand scheme of things, though, it doesn’t move a whole lot for most players once they’ve reached a plateau in their skill development.

The ranking system is a measure of skill and activity over a shorter term: a single season now that the ranked update is out. It’s loosely tied to MMR, but also speaks to activity in the season. Rank is purposefully more volatile than MMR so you can see larger gains quickly when you get on a hot streak (the corresponding cold streaks that come along with that aren’t quite as entertaining). Over a long enough period, rank and MMR converge, but over a shorter period, rank allows for a lot more movement than MMR does. There’s a balance to be found there, though, to avoid rank diverging too much from MMR. That’s where things like bonus points come into play, which nudge players toward the rank that directly maps to their MMR. At any time, about 4 in 5 players are ranked within a single division of where their MMR says they should be. 19 in 20 are within 2 divisions.

To give an example of the difference between the two, when we were developing the new ranked system, one of the bits of data I worked with was looking at how much a player’s MMR changed over the course of 3 months. For the vast majority of players, when you map that against where we’d expect that MMR to be in terms of rank, their MMR at the start of the period and their MMR at the end of the period were within the equivalent of 1/10th of a single rank. I’m sure some players would appreciate that since rank would be a nearly perfect representation of skill, but I believe most players would be frustrated with such little visible results for their played time.

MMR is also a pretty hardcore concept. Our forum and Reddit community are the perfect audience for it, but it can be a confusing concept for many players. Ranks provide a friendlier way to present similar information. They also allow us to do things that you really can’t do with MMR as it would destroy the integrity of the measurement: promotions/demotions, rank penalties for leavers, etc.

It’s worth noting that giving players a way to see their MMR is on our to-do list. It’s useful and interesting information for dedicated players. Something I definitely want to do.