It is because of inertia of motion.That is, when a body is moving it has a tendency to remain in that state.For example,when you are cycling after pedaling for some time ,you stopped pedaling.But the cycle does not stop  at once because of inertia of motion.Only after  it goes some distance does it stop.This same thing happens when you are pushing a box.

If this answer was helpful for you ,please select it as the best answer.
6 4 6
Frictional concept also takes place here. :)
Because the box is at  stationery object and it takes more force to push it and stationery object takes more force 
1 2 1