Aspect ratio is a powerful indicator of the general performance of a wing. Much of the drag created by a wing, notably at low speeds, comes from an effect called induced drag which occurs at the wing-tips. High pressure air on the bottom has a "short cut" to the low-pressure air on top by circling around the tip of the wing. This causes a vortex to form, which robs the plane of energy. By reducing the amount of wing tip area, making it skinny or pointed for instance, you reduce the amount of energy lost to this process, and thus reduce effective drag. This is why high performance gliders have very long, skinny wings; they cannot compensate for induced drag by increasing engine power.
Why don't all aircraft have high aspect-ratio wings? There are two main reasons: