From Earth's point of view, eclipses can be:
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[?].
As seen from Earth, an eclipse can only occur when the Sun, Earth and Moon 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.
The following web page lists many of the cycles over which solar and lunar eclipses repeat, including the Saros and Inex. http://www.phys.uu.nl/~vgent/calendar/eclipsecycles.htm