The Sun appears in the sky to us, shining with its own light. The Moon, on the other hand, “shines” due to reflected sunlight. The appearance of both the Sun and the Moon can be affected by the shadows cast by the Earth and the Moon in the sunlight.
The apparent motion of the Sun and Moon across the sky (as viewed from Earth) is due to a combination of the rotation of the Earth, the orbit of the Moon about the Earth, and the orbit of the Earth-Moon system about the Sun. One unusual aspect of the Moon’s orbit is that its rotation rate is synchronized with its orbit (the time for one rotation on its axis is the same as the time for one orbit), so that it always presents the same side to the Earth, regardless of where the Moon is along its orbit.
The Moon is only illuminated on the side closest to the Sun. When the Moon is observed from Earth different amounts of that side are illuminated depending on where the Moon is on its orbit around the Earth and where the Sun is with respect to your viewing location. About once a month we see a completely illuminated (Full) Moon which occurs when the Sun and Moon are on opposite sides of the Earth. Approximately two weeks later the Sun and the Moon are on the same side of the earth, and the only part of the Moon facing the Earth is on the “night” side of the Moon (New Moon). This lunar cycle continuously repeats through all the phases of the Moon, and historically has been an important part of calendars. Thus the phases of the Moon as viewed from Earth are caused by the Moon’s position along its orbit.
At first glance, it might seem that every month during a New Moon the Moon should line up perfectly with the Sun and block the Sun from Earth’s view causing a Solar Eclipse. Similarly during a Full Moon the Moon should fall directly within Earth’s shadow causing a Lunar Eclipse. However, the Moon’s orbit has a slight tilt (with respect to Earth’s orbit about the Sun), so that usually the New Moon misses the Sun in the sky and usually the Full Moon misses Earth’s shadow. Astronomers refer to the line where the plane of the Moon’s orbit intersects the plane of Earth’s orbit as the Line of Nodes, and this can be thought of as the axis of the tilt of the Moon’s orbit. In order to have an eclipse the timing of orbits has to be just right: the Moon has to be crossing the Line of Nodes at the same time that the Line of Nodes is lined up with the Sun for an eclipse to occur.
Suppose the orbit of the Moon around the Earth was not tilted at all with respect to the orbit of the Earth around the Sun. How often would Lunar Eclipses occur? How often would Solar Eclipses occur? Would the answer to either of these questions depend upon if you lived at the North Pole or on the equator?
Solar Eclipses are rarer and thus harder to predict than Lunar Eclipses. Think about how the size of the Moon’s shadow compares the size of the Earth’s shadow and how this might affect how often the two different types of eclipses occur.