An eclipse occurs when an astronomical body such as a planet, or satellite gets between a source of light (e.g. the Sun) and another body. For instance, Jupiter eclipses its moons when it gets between them and the Sun.
The most dramatic eclipses from earth are:
Total eclipses occur where the light source is totally blocked off by the eclipsing body. For total solar eclipses, the viewer is in the umbra part of the moon's shadow.
Partial eclipses occur at places where only part of the luminary is covered (solar eclipses), or when only part of a body is eclipsed by the shadow (lunar eclipses). For solar eclipses, the viewer is in the penumbra part of the moon's shadow.
An annular eclipse is a total eclipse of luminary where a thin ring of light is visible around the intervening object. It is sheer coincidence that the Moon and Sun have nearly equal apparent sizes, making annular eclipses possible. Annular eclipses are ideal times for observing solar prominences.
An eclipse involving the Sun, Earth and Moon can only occur when they are in a line. Because the plane of the orbit of the Moon is tilted with respect to the plane of the orbit of the Earth (the ecliptic), eclipses occur only when the three bodies are near the intersection of these planes: these are nodes. The Sun passes either node once a year, and eclipses occur in a period of about 2 draconic months around these times. There can be from 2 to 7 eclipses in a calendar year. They repeat according to eclipse cycles.
Before modern astronomy there were explanations eclipses in every culture of long standing. These would typically involve conflicts between mythic forces. At the Imperial observatory, Bejing is a carved stone brought from a distant province with the following explanation (here rewritten): "This carved stone chart explained the cause of solar eclipses. The center of the golden bird (the symbol of the sun) was covered by the toad (the symbol of the moon). The people of the Han Dynasty called the phenomenon a good combination of the sun and the moon." In this explantation we see a recognition of the celestial realities and a cheerful outlook regarding the event. In other cultures an eclipse could be both a surprising and a terrifying event.
The following web page lists many of the cycles over which solar and lunar eclipses repeat, including the Saros and Inex :