An annular eclipse is the term given to a solar eclipse during which the Moon passes directly in front of the Sun but, due to its position in its ellipitical orbit, cannot completely cover the star. The result is the dark circle that is the Moon surrounded by a thin ring of intensely bright light that is the part of the Sun which the Moon could not obscure. Since this annular phase is so bright, the Sun's corona cannot be seen (unlike in a total eclipse, during which the corona can be seen but the star itself cannot).
The mean distance from Earth to the Moon is 384,467 kilometers (238,866 miles) but, since the Moon's orbit is ellipitic rather than circular, the distance of the Moon from Earth varies from as close as approximately 353,600 kilometers (221,000 miles) to as far as approximately 403,200 kilometers (252,000 miles). When the Moon is closer to Earth, it appears larger in the planet's sky and vice versa. As a result, a solar eclipse that occurs when the Moon is closest (or near closest) to Earth will be total: The Moon will appear large enough to block out the entire star for a brief moment, leaving only the corona visible. A total eclipse creates the illusion of a black sun that continues to shine. Should a solar eclipse occur while the Moon is far enough away from Earth that the Moon doesn't appear at least as large as the Sun, an annular eclipse will occur. Since the Moon cannot block the entire Sun at its distance, a thin ring of the Sun is still visible around the darkened lunar disk.
Due to the Moon appearing smaller during an annular eclipse, the shadow of the Moon created by the Sun (known as the umbra) isn't long enough to reach Earth. The shadow that does reach Earth is the antumbra, a 'negative shadow,' which forms in the penumbra (the partially shadowed area created during an eclipse). The antumbra is a widening cone of shadow (unlike the umbra, which is thinner the farther away from the Moon it is) which, when it reaches Earth, will still be very thin. As the Moon and Earth rotate, the specific area of the planet engulfed by the antumbra changes. The path the antumbra moves along is known as the path of annularity. Only within the path of annularity can an annular eclipse's annulus (the ring created by the Sun's still visible edge) be observed. Other regions of Earth within the partial shadow penumbra will see only a partial eclipse.
The path of annularity, though it can stretch over 14,000 kilometers (8,750 miles) in length, won't likely exceed more than 80 kilometers (50 miles) in width, if even that. The annular eclipse which occurred on 10 June, 2002 (for example) had a path of annularity that only reached 78 kilometers at its widest (and 13 kilometers at its thinnest). The vast majority of this eclipse's path of annularity was located over a thin piece of the Pacific Ocean. The penumbra, where a partial eclipse could be observed, while also mostly over the Pacific Ocean, also managed to include eastern Asia, northeastern Australia, and most of Canada, the United States, and Mexico. Annularity during an eclipse such as this can last up to 12 minutes but typically lasts only six.
The next annular eclipse has been predicted to occur on 31 May, 2003.
Sources:
http://sunearth.gsfc.nasa.gov/eclipse/ASE2002/ASE2002.html
http://nssdc.gsfc.nasa.gov/planetary/factsheet/moonfact.html
http://www.mreclipse.com/Special/SEprimer.html