Rushing in football is the act of an offensive player running with the ball with the goal of advancing towards the end zone. The two ways to advance down the field is either by passing or by running with it (rushing), and any play that does not involve a passing action is considered to be a rush. It is good for a team to have variation between passing and rushing plays, otherwise offense can become predictable and easily defended. A rush can be called just a run or a carry, and it is not unusual for commentators and TV analysts to use those terms on broadcasts.
The statistic that measures rushing is called "rushing yards," and it can be calculated for teams or players during seasons or individual games. Running backs are the players that rush the most and so lead the league in rushing yards, but quarterbacks and wide receivers also often rush. Some quarterbacks love to rush, while others do not; it is very personal and it varies a lot from player to player. But regardless of a quarterback's like or dislike for rushing, he will have to do it eventually. Quarterbacks usually rush when all the passing options are well marked and a gap opens up. In that case, quarterbacks often choose to end the play with a dive or a slide, in order to escape a rough tackle that can follow a good rushing play.