Sometimes the last couple of minutes of a football/soccer game are really boring. One team is up 3 goals and there isn't much time left on the clock, the game is basically over even if it will take a couple more minutes before the game is technically over. This is a problem from a satisfaction standpoint. The thrill of victory gets thinly spread over those minutes between when the game is basically over and technically over, and the losing team just gets to be stuck in an unwinnable game. We want victory to have impact, and we want the game to continue to feel competitive until the very last moment as being trapped in an unwinnable game feels shitty for one team and boring for the other.
We want the game to get more exciting as the timer whittles down to the last couple seconds, not less. That means keeping the match competitive until the very last moment. A sport that does this well is baseball.
Baseball isn't timed like soccer/football, instead each team gets as much time as they need but can only fail so many times (each "out" is a failure in this context). Notable in this model is that while there is a limit to how often you can fail, there is no limit to how often you can succeed. You can score an infinite amount of runs without getting a single out. This means that until the final pitch both teams have a realistic path to victory. Even when it is unlikely, it is there, and that presence makes the match more interesting and tense as it nears its end.
Most of the maps in Overwatch are based on a timed challenge. One team tries to take over a series of points and the other team tries to deny them those points for a couple of minutes, or one team tries to push a cart and the other team tries to stall them for a couple of minutes. Given that these challenges are timed you would think that the matches have the same problem as soccer/football where the end of the match becomes boring and pointless. That there would of come a point at which there is no longer enough time to push the cart as far as it needs to go or to capture a point even if everyone was there to do it. Overwatch though avoids this problem by having Overtime.
If you are the team pushing the cart then so long as there is someone on the cart the game won't end, ever. Same for point capture, so long as you have someone contesting the point you haven't lost. The cart won't go forward if an enemy is also on it, but the game will stay in overtime as long as it needs to.
As you complete objectives the Overwatch gives you more time. It would of been easy for them to give you 10 minutes to accomplish 2 things but instead they give you 5 minutes to accomplish the first objective and then add another 5 minutes when you have so you can go for the second objective. The point of doing this is to prevent the games from dragging on. If the attacking team is doing very poorly then lets call it and move on.
Overwatch structures each match to be always be as interesting as possible by cutting out as much of the dead air as it can. It keeps hope alive for both teams until the very last moments, and end the game as quickly once that hope dies. Overwatch doesn’t drag out the games and force players to watch themselves die slowly.