How does MMR work?

I was looking at my ranks from previous seasons and I noticed that in Y3S4 I was Silver 2 with 2652 MMR then next season (Y4S1) I was Bronze 2 with 2500 MMR and this season I'm Bronze 1 with only 2000 MMR.

Is there a reason that the amount of MMR I need to rank up is changing?

Matchmaking rating and ranks contains all the answers. This is the most important picture from there (X axis is MMR, Y axis is number of players):

Players ranks will always be distributed like on this graph. However, player number and performance varies from season to season.

Let's imagine following situation. In season N Bronze started with 2500 MMR. Everyone below 2500 is in Copper ranks. But in the next season N+1 there are much more new players within Copper category. To keep distribution the same, some number of top players in Copper category is promoted to Bronze category. This effectively moves Bronze lower bound into let's say 2000. So thresholds or bounds are still there, but they are updated periodically so total distribution of player ranks always looks the same.