Why do players sometimes run after the ball after they score a goal?
There are mainly two reasons why players go for the ball right after scoring a goal.
The most common reason is to speed up play and it is employed by teams that are still trailing or have just drawn level following the goal, with the game in its final minutes. The opponent players will show little haste in returning the ball to the centre for a kick-off, thus slowing down the game and preventing a loss or draw, as the case may be. The goalscorer, usually being closest to the ball, grabs the ball and returns it to the centre promptly so that their team can have another chance at scoring a goal in the limited time available.
Players sometimes use the ball as a prop in their celebrations. The most popular variant of a celebration involving the ball is tucking it under their shirt usually to signify the pregnancy of a loved one. Lionel Messi did it after scoring for Argentina against Ecuador and there are countless other examples of players doing it for this reason.