Why do phases exist, and why are eclipses so rare? Spin the Moon around Earth (its real orbital inclination is 5.14°) and rotate the line of nodes — the place where the Moon's tilted orbit crosses the ecliptic. When a new or full moon lands near a node, the shadows line up and you get an eclipse; anywhere else the Moon sails above or below the shadow and nothing happens.
The Moon orbits Earth every 27.3 days, but its orbit is tipped 5.14° to the ecliptic — the plane Earth travels around the Sun. Half the month the Moon is above the ecliptic, half below, and it crosses the plane only at two opposite points: the nodes, joined by the line of nodes. A lunar eclipse needs a full Moon sitting inside Earth's shadow (real umbra: ~4,600 km wide at the Moon's distance, and the Moon is 3,474 km across — it fits, just barely). A solar eclipse needs a new Moon's shadow to reach Earth. Because the node line points in a fixed direction while new/full Moon wanders through every position, an eclipse needs the two to line up within a few degrees — roughly twice a year, each type, somewhere on Earth. The shadow cones and bodies below are drawn enlarged (×6 for visibility); the readouts show the true km values.