It's really quite simple. You have a stick. At one end is a rock and at the other end is a magnet. The stick is physically held in place such that movement at the rock end is mirrored at the magnet end (think of a see-saw). Additionally, the magnet end of the stick is surrounded by thin wire metal coils. As the rock end of the stick is dragged through the undulations of the record disc it moves in both the horizontal and vertical planes. At the magnet end of the stick this movement generates a small electric current through the surrounding coils which is then carried via an interconnect cable to a phono preamp.
Based on this description, the purpose of tracking force is to keep the rock (stylus tip) in contact with the record groove walls and to keep the magnet centered within the surrounding coils. Cartridge manufacturers usually give a range for tracking force. It's a little like tire pressure in cars. Depending upon what type of ride you like, the roads you drive on and your driving style the "correct" tire pressure could be a the low or high end of the recommended range. Tracking force is ultimately set by ear.
See these links for detailed explanations of all the other factors (SRA, VTA, azimuth, tracking error, etc.) that effect cartridge setup and sound quality:Walker AudioLaura Dearborn/van den HulGood SoundsAudiophiliaAudio & Music Bulletin