We start by assigning a point value to each situation on the football field by the average number of points teams score in those situations: 1st and 10 at the 50 is worth 2.89 and 2nd and 3 at the opp 43 is worth 3.22. We can then assign a point value to a play based on the expected points before and after a play - 7 yards on 1st and 10 at the 50 is worth .33 = 3.22 - 2.89.
We can then attach that value to players based on their participation in the play. If we add up the EPA for the entire team over the course of a game, we get that team's score minus the expected value of each possession at the beginning of the drive. Related to the EPA is the NEPA (net expected points added) which also accounts for the impact of the play on the expected the opponent will score on their next possession.