A total solar eclipse, as its name implies, is what happens when the Moon passes between the sun and the Earth, when the Moon is closest to Earth in its orbit. Historians usually cite June 15, 763 BC as the earliest record of such an event, based on an ancient Assyrian text. The most recent total solar eclipse occurred on July 11, 2010, and we won't see another until November 13, 2012.
A partial eclipse, in contrast, means that the Sun and Moon are not perfectly in conjunction, so the Moon can't completely block out the sun. The most recent partial eclipse happened on November 25 of this year, mostly visible in the southernmost part of the world.
During an annular eclipse, you get the critical conjunction, but the Moon is too distant from the Earth in its orbit to completely block out the sun. Instead, you get a very bright ring around the moon. This will next occur on May 20, 2012.
Langton's novel opens with one of the finest descriptions of a total solar eclipse in modern literature, with passing references to the solar corona, Baily's beads (notably seen in the opening credits of the TV show Heroes), shadow bands, and the diamond ring effect, "the flash of red light at the very end" - all very real phenomena that occur during an eclipse.