The lunar nodes are the orbital nodes of the Moon, that is, the points where the orbit of the Moon crosses the ecliptic (which is the apparent path of the Sun across the heavens against the background stars). The ascending node is where the moon crosses to the north of the ecliptic. The descending node is where it crosses to the south.
Eclipses occur only near the lunar nodes: Solar eclipses occur when the passage of the Moon through a node coincides with the new moon; lunar eclipses occur when passage coincides with the full moon. A Lunar Eclipse may occur if there is a full moon within 11° 38' (Celestial Longitude), of a Node, and a Solar Eclipse may occur if there is a new moon within 17° 25' of a Node.
The lunar nodes precess rather quickly around the ecliptic, completing a revolution (called a draconitic or nodical period, the period of nutation) in 6793.5 days or 18.5996 years (note that this is not the same length as a saros).