An eclipse is really a question of line-up. See how the Sun, Earth and Moon arrange themselves for a solar and for a lunar eclipse, and how the dark umbra and the pale penumbra decide whether the eclipse is total or only partial.
An eclipse happens when one body comes between another body and the Sun, so that the Sun's light is blocked and a shadow is cast. There are two we can see from Earth. In a solar eclipse the Moon comes between the Sun and the Earth; in a lunar eclipse the Earth comes between the Sun and the Moon.
Every blocked body throws two cones of shadow. The dark inner cone is the umbra, where the Sun is completely hidden and the eclipse is total. The pale outer cone is the penumbra, where the Sun is only partly hidden and the eclipse is partial.
The top row shows a solar eclipse: the Moon sits in the middle and its small umbra just reaches the Earth. The bottom row shows a lunar eclipse: the Earth sits in the middle and its wide shadow reaches all the way to the Moon, which turns dark as it moves into the umbra.
The same geometry explains the phases we see and why eclipses are rare. The Moon's orbit is tilted, so most months the three bodies miss a perfect line-up — which is why eclipses come in short seasons rather than every month.
For a solar eclipse the Moon passes between the Sun and the Earth. From a small area of the Earth's surface the Moon then covers the Sun, and daylight dims to a strange twilight.
Because sunlight arrives as a broad beam, the Moon stops the rays that hit it and lets the rest pass by. A shadow is cast behind the Moon, and that shadow is what sweeps across the Earth during the eclipse.
The Moon's shadow is really two cones. The dark inner umbra is small and just reaches the Earth, so only a narrow track sees a total eclipse. Around it the pale penumbra covers a much wider area, where the Sun is only partly hidden.
A lunar eclipse happens about two weeks later, when the Moon has moved around to the far side of the Earth. Now the Earth is the body in the middle, and it is the Moon that can enter a shadow.
The Earth is far bigger than the Moon, so the shadow it throws away from the Sun is wide. When the Moon moves into it, the whole Moon can be covered at once, and it dims to a dark, often reddish, disc.
What an observer sees depends on which shadow they are in. Inside the umbra the eclipse is total; inside the penumbra it is partial, with the Sun or Moon only partly covered.
Because the Moon's orbit is tilted by about five degrees relative to the Earth's path around the Sun. Most months the Moon passes a little above or below the straight Sun–Earth line, so its shadow misses the Earth and the Earth's shadow misses the Moon. Only when the alignment is nearly perfect does an eclipse occur.
The umbra is the dark inner cone of shadow where the blocking body hides the Sun completely. An observer inside the umbra sees a total eclipse: the Sun fully covered, or the Moon fully in the Earth's shadow.
The Earth's atmosphere bends and filters sunlight that grazes its edge, letting mostly red light through into the umbra. That faint red glow falls on the Moon, giving it a coppery colour during a total lunar eclipse.
No, because the two line-ups are different. A solar eclipse needs the Moon between the Sun and the Earth; a lunar eclipse needs the Earth between the Sun and the Moon. Those are opposite arrangements, so they happen at different times, usually about two weeks apart.
By coincidence the Sun is about 400 times wider than the Moon but also about 400 times farther away. The two therefore look almost the same size in the sky, which is why the Moon can just cover the Sun during a total solar eclipse.