Is this how you get endurance?

i am 13, 6'0, 143-152 pounds, and a pretty good runner(fast and can go pretty long). so lets say you are running, when you are felling tired, you push yourself to go longer. what i am trying to find out is if you push longer and harder, do you get more endurance than when you just stop when your tired. and when your tired, is your endurance going up?