Wings generate lift due to the motion of air around them, so moving more air generates more lift. Larger wings move more air, so larger wings generate more lift than smaller ones -- as one would expect. In addition, higher speed means any particular wing will move more air, so flying faster also generates more lift. The two effects are linked however, larger wings also generate more drag, slowing the airplane down. For this reason the "right" wing for any design is highly dependant on the speeds that the aircraft will fly at. Designs for lower-speed use will want larger wings, and lower wing loadings. High-speed designs will want smaller wings to reduce drag, and therefore have higher wing loadings.
Wing loading is a useful measure of the general maneuvering performance of an aircraft. To manuver and aircraft the wing must generate extra force, lift, which it does by increasing the angle of attack. This has the side effect of also increasing the induced drag, slowing the aircraft down, which has to be offset by increasing power. For any particular design there is a maximum amount of manuvering that the engine can make up for, known as the sustained turn performance. Planes with lower wing loading will not have to increase their angle of attack as much in order to supply any particular amount of lift, so lower wing loading leads to higher sustained turn performance. This is the primary explaination for the famous difference in manuverability between the Supermarine Spitfire and Messerschmitt Bf-109, the later used much higher wing loading in order to reduce drag for higher speeds, but in doing so limited its manuverability (which the German pilots did not consider important).
Wing loading is also an important general indication of the smoothness of the ride of a particular design. Planes with higher wing loadings will not be effected by turbulance as much as one with lower wing loading. Since turbulance is primarily an effect of interactions of the air and ground, for low-altitude high-speed flight a higher wing loading will lead to a much smoother ride. This is the reason the F-15E is considered a poor compromise, the plane was originally designed for manuverability and has a low wing loading (for a fighter), which makes the E version rather taxing at low altitudes.