Aircraft land on the main wheels. For aircraft with a nose wheel the main wheels are the back ones, but for aircraft with a tail wheel (also called “tail-draggers”) the main wheels are in front. In either case, the main wheels are very close to the centre of gravity and carry most of the aircraft's weight. When they are not the main wheels, the nose or tail wheel only carries a small fraction of the weight.
The aircraft must land on wheels that are close to the centre of gravity (longitudinally). If they were not, the force on the wheels would create momentum that would violently pitch the aircraft. Actually, tail-draggers tend to bounce on landing a bit because there still is some momentum left, and in case of tail-draggers it pitches the aircraft up.
Early planes were all tail-draggers, because that layout is more robust, handles unpaved runways better and has less drag when the gear is fixed. This wheel configuration, however, provided poor directional control, especially once the tail lifted off the ground during take-off.
Later designs started to use nose-wheel, because it provides better directional control, is directionally stable and with invention of retractable landing gear the drag didn't matter any more.