A total lunar eclipse is an event in which the Moon passes directly through the Earth’s shadow. A total lunar eclipse will always occur on a night of a full moon.

The Moon does not completely disappear in the shadow of our planet because of the refraction of sunlight by our own atmosphere.
Because this sunlight has to pass through our atmosphere (also influenced by both dust and clouds) it is scattered.

As red light has the longer wavelength it is less scattered than for example blue light, this effect causes the distinctive red colorization of the Moon during an eclipse.
It is also the same effect that causes the red sunsets and sunrises.