Answer:
A few examples.
After 8 hours of classes, you grab the door handle and start pushing on it, harder and harder, not realizing you have to pull. Applied force is how much you can exert on the door, plus the reaction of the frame. net force is zero - the door won't budge.
Indiana Jones, while trying to grab yet another treasure that belongs in a museum, triggered a trap and a sack weighting 600N is pushing over his head. Due to his old age he's not in shape, and he manage to push back with only 500N of force. Applied force is 600N from the weight, and 500N from the archeologist. With a net force of 100N towards the old man head.
Mario and Luigi have ran out of gasoline in their car, so they're stuck pushing. Due to being in peak condition, each one applies 800N to the side of the car, dragging it forward. Applied force is 800N from each plumber, and net force is 1600 N.