Guitar string specifications like "medium," "light" and "extra light" refer primarily to the thickness of the string. Thickness, in turn, determines how much tension has to be placed on a string before it will vibrate. The less tension, the easier the string is to play, but the more likely you'll hear buzzing or overtones from the string. Essentially, then extra-light strings are designed to be easier to play and brighter-sounding than light strings.
Extra-light strings have a smaller diameter than light guitar strings. For instance, the low E string in a set of light acoustic guitar strings is typically 0.053 inches in diameter; the same string in an extra-light set would be 0.047 inches. One the other end, a high E string would be 0.012 inches in diameter in a light set and 0.010 inches in an extra-light set.
While the differences in diameter between light and extra light strings may be just two or three thousandths of an inch, they make a big difference in string tension. A light low-E string must be tensioned to 11.8 Kilogram to bring it up to the proper pitch; an extra-light low-E need only be tensioned to just over 9.07 Kilogram -- a 6 pound difference. Try lifting a 6-pound weight with one finger and you'll get a sense of how much of a difference it can make in playability.
Another important aspect of a guitar's playability is its action, or the distance between the fretboard and the strings. String gauge plays a role here, because the more tension on the strings, the more the guitar neck will bow backwards, creating a larger gap under the strings. A full set of extra-light strings exerts about 13.6 Kilogram less tension on the neck than light strings, thus making it easier to press the strings and reducing the distance they must be pushed.
Sustain and Tone
While extra-light strings have an advantage in terms of playability, light strings offer a louder, fuller tone, primarily because there's just more steel and bronze vibrating in them than in extra-lights. By the same token, the light strings will have a tendency to vibrate longer, because their greater mass contributes to longer vibrational inertia. This longer vibration time is known as "sustain," and allows you to play more slides, hammer-ons and pull-offs per string pluck than is the case for lighter-gauge strings.