Warning: Technobabble ahead. Proceed at your own risk
The imaginary line drawn from the center of the Earth to the center of the Sun, and projected against the backdrop of the Stars is called the “Ecliptic”, because, when an eclipse occurs, the Moon must be at some point on this line in alignment with the Earth and Sun. The Ecliptic passes through the 12 signs of the zodiac.
The Earth’s equator, when projected against the backdrop of the stars defines the “Celestial Equator.” The Earth’s rotational axis is tilted by about 23½ degrees from the plane of the ecliptic, and, therefore, so is the Celestial Equator.
The plane of the Moon’s orbit is tilted by about 5 degrees from the ecliptic, in contrast to most other moons in our Solar system which (other than captured asteroids and such) orbit within a few degrees of the primary’s equator (cf. Jupiter and Saturn.)
Due to an amazing cosmic coincidence, the angular extent of both the Moon and the Sun, as seen from the surface of the Earth, are almost exactly equal, and about ½ degree. Both may vary a bit, as the orbits of neither the Earth nor the Moon are perfect circles, and as we get closer or farther from the Sun, its apparent diameter grows or shrinks (by a very small amount.) The same with the Moon.
As the Earth-Moon system orbits the Sun, occasionally the Moon passes directly between the Earth and Sun, causing a solar eclipse. But, since the center-to-center distance between the Moon and Sun (as viewed from the surface of the Earth) can be as much as ±5 degrees, and each is only ½ degree, more often than not the Moon will pass far “above” or “below” the Sun. Sometimes, when we are nearer than usual to the Sun (making it appear slightly larger) and the Moon is farther than usual (making it appear slightly smaller), when the two are aligned center-to-center, the Moon does not completely block the disk of the Sun, and a thin ring, or “Annulus” (Latin for “ring”) of Sun shows around the silhouette of the Moon. Annular eclipses are slightly more common than total solar eclipses.
At the average distance from the Earth that the Moon orbits, the central, darkest part of the Earth’s shadow (the “Umbra”) is a few degrees wide. Most months, at the time of a full Moon, the Moon is passing well above or below the Earth’s shadow. On average, about twice a year the Moon passes into the shadow, but not always into the central umbra, and at these times there is a “Penumbral” eclipse (pen (from Latin paene, near) + *umbra *(Latin for shadow)).