To open a door, you push on the part of the door that is farthest from the hinges. Why would it be harder to open the door if you pushed on the center of it?
Because of the torque that is the "rotational equivalent" of a force.
Opening a door you exert a force but you have to make the door ROTATE. This is a little bit more complicated than simply push the door, say, on a straight line because it involves the RADIUS! The bigger the radius of rotation the bigger is the torque you exert!
So, basically, you'd need a bigger force to rotate the door applying it too near the hinges!