Eclipses take place when the Sun is partially or completely blocked from view by some body passing in front of the observer. In a solar eclipse, the Moon passes between the Earth and Sun, and observers in the shadow of the Moon see an annular, partial or total solar eclipse. In a lunar eclipse, the Earth passes between the Moon and Sun, and observers (on the Moon) in the shadow of the Earth see a total or partial solar eclipse, while observers on the Earth see a penumbral, partial, or total lunar eclipse.
If the orbit of the Moon around the Earth were in the same plane as the orbit of the Earth and Moon around the Sun, there would be an eclipse of the Sun at every New Moon, and an eclipse of the Moon at every Full Moon; but because the Moon's orbit is tilted (by about 5 degrees) relative to ours, the Moon usually passes above or below the Sun at New Moon, and above or below the shadow of the Earth at Full Moon, and there are no eclipses, even though the Earth, Moon and Sun are more or less "lined up". However, there are two periods, separated by about six months, when the Moon is very close to the Ecliptic, instead of being well above or below it, and we must have eclipses of the Sun at New Moon, and of the Moon at Full Moon (in fact, the origin of the term Ecliptic to describe the Sun's apparent path in the sky is due to the fact that eclipses occur only when the Moon is close to the Ecliptic). Periods when eclipses can (or must) occur are called eclipse seasons, and are about 40 days long. Since this is longer than the cycle of lunar phases (which is 29 1/2 days), there must be at least one New Moon and at least one Full Moon during each eclipse season, which means there must be at least two solar eclipses and two lunar eclipses every single year, for at least four eclipses a year. There are often, in fact, five or six eclipses a year, and on occasion, seven. So eclipses of the Sun and Moon are not particularly "rare". They don't happen every day, or even every month, but they do happen frequently enough to be considered a relatively commonplace occurance.
(to be covered later, on this and the corresponding pages about Solar Eclipses and Lunar Eclipses):
(1) The geometry of lunar eclipses -- penumbral, partial and total -- and their appearance. How that geometry determines the likelihood of seeing a given eclipse.
(2) The geometry of solar eclipses -- partial, annular and total -- and their appearance. How that geometry determines the likelihood of seeing a given eclipse, making solar eclipses seem much rarer than they are.
(3) Eclipse Seasons, and their relationship to lunar and solar eclipses.
(4) Changes in the orbit of the Moon which change the timing of eclipse seasons.
(5) Long-term changes in the orbit of the Moon, which will eventually make total solar eclipses impossible.