Points

Your number of points is what decides your place in your division. After having completed your placement matches, you start out with 0 points[4]. These points only decide your place within your division, and there is a hidden "Matchmaking Rating" (MMR) as well, which decides which opponents you will face. Since there are no global or regional rankings, the displayed score isn't an accurate measure of skill[5] when compared to anyone else. This is because the visible rating does not match the hidden MMR rating, and is influenced by the Bonus Pool. Each play-season the visible rating will be reset, while the MMR rating stays intact. This makes it even harder to derive the true skill of the player.[6]

Earning and Losing Points
You earn or lose points by winning or losing matches, respectively. To simplify how it works in practice[7]:

y = (+/-)12 + x + z

where

"y" : the total number of points
"x" : the relative expected skill level between opponents (weighted difference in MMR which can be negative)
"z" : the points you get from your bonus pool
=> "x" is a value in the interval of [-10,10], positive numbers are when your opponent is favored

if the game says you are even, "x" is part of {0,1}
if it says your opponent is slightly favored, then "x" is part of {2,3}
if it says your opponent is favored, then "x" is part of {4,5,6,7,8,9,10}
(of course, if you are the slightly/favored player, then "x" is negative, which means you will lose more than 12 points)

"z" will be be greater than zero when

your bonus pool is >0
you are victorious
If these 2 conditions are met, then Z will be equal to 12+x, permitted you have enough points in your bonus pool.

Bonus Pool
The bonus pool is the sum of all "bonus points" you can get, which are added to the rating points you earn after a victory. They are there to give the player a catch-up boost if they haven't played in a while, in other words, they serve as a means to keep up with the inflation of points in the league.

Your bonus pool seem to not be reset once you move up (or down) a league, as your initial rating in that league should reflect your calculated rating at that point in time.

Hidden "Matchmaking Rating" (MMR)
In addition to your points, there is also a hidden Matchmaking Rating, presumed to be very much like the WoW Arena Matchmaking System. This rating decides which opponents you will meet, and tries to quantify your skill level. It (presumably) takes into consideration when you have winning streaks or losing streaks. Moreover, it is this MMR that decides if you're eligible for a promotion or a demotion. The aim for the MMR is to rank you in such a way that you have ~50% win rating. You presumably start out at 0 and then your MMR climbs to the level of the people against which you win roughly 50% of the time.[8]