An eclipse occurs when the Sun, Moon and Earth are in a specific position with each other. They need to lie not only in the same plane together, but also in a straight line. This alignment, "Syzygy", can only take place when the Sun and Moon are in conjunction at New Moon or in opposition at Full Moon. The plane of the Moon's orbit is inclined to the plane of the Ecliptic (the apparent path of the Sun around the Earth from a geocentric point of view) by an angle of approximately 5 degrees. Therefore, this alignment cannot take place every month. Eclipses occur only twice a year when the Sun and Moon are near the Lunar Nodes. The Sun and Moon don't have to be exactly conjunct the Nodes for an eclipse to occur.

There is an eclipse season about every six months (173.3 days) and the length of a season is about 36 days. Usually eclipses come in pairs and each season contains one Solar Eclipse and one Lunar Eclipse, but not necessarily in this order. There are at least four eclipses every year, sometimes more, the maximum number of eclipses in a year is seven.

The word "eclipse" comes from the Greek word meaning "disappearance".

References:

Mary Dowton and Steve Cahill. The Astrologer's Textbook of Astronomy
Bernadette Brady. Predictive Astrology - The Eagle and the Lark
Rose Lineman. Eclipse Interpretation Manual

NASA Eclipse Home Page
Sky and Telescope Eclipses Page