Did Not Finish (DNF) refers to a match that has not been finished either because of a direct network disconnection or any failure that caused the disconnection. The term "Did Not Finish" is coming from the real life forms of racing, including automotive racing, horse racing, cycling, track and distance running, and skiing, and denotes a participant who does not finish the race due to any failure.
In FUT, disconnecting from matches affects your DNF Modifier which could reduce the number of coins and rewards you receive from future matches. In other online game modes than FUT, a DNF could cause you a loss even in a match that you were wining it.
DNS Modifier is a built-in program in FIFA games that monitors your DNF rates and reduces the amount of coins and rewards you gain from your online matches as your DNF rate goes higher.