An eclipse requires an alignment of three celestial bodies, the Sun, Earth and Moon. Lunar eclipses are occultation of the Moon by the Earth's shadow while solar eclipses are eclipses of the Sun in the shadow of the Moon.
These celestial concordances are frequently observed, at least one of each (lunar eclipse and solar eclipse) every 6 months. The Moon appears to us with phases, i.e. in different lights of the Lunar sphere.
As the moon only reflects light from the Sun, the only visible part of the Moon is one that is geared towards both the Earth and to the Sun.
The periodicity of phases of the moon is 29.5 days, or a lunation or lunar month although there are several lunar month. Eclipses take place at syzygies, i.e. when there is a quasi alignment between the Sun, Earth and Moon. The eclipse occurs at new moon, the lunar eclipse occurs at full Moon.
Cycle periodicity of eclipses is known as Saros. A cycle that obeys surprising coincidences and an average Saros eclipse contains 84, 42 solar eclipses and 42 lunar eclipses. Indeed, during this cycle, there are the same number and the same type of eclipses, total, annular, partial every 223 lunation or every 18 years. More precisely, the Saros is a period of 6585.32 days or 18 years, 10 or 11 days and 8 hours, depending on the interval contains 4 or 5 leap years.