It is due to the scattering of light, by the particles of the Earth's atmosphere.
When the moon is near the horizon, the moonlight needs to travel a larger distance, than when it is directly overhead.
So, when the moonlight (made of white light) reaches you, the blue, green and purple parts of the light gets scattered, leaving the orange, yellow and red parts of it.
Therefore, it seems to appear reddish in colour.
This is similar to the redness of [the Sun](https://socratic.org/astronomy/our-solar-system/the-sun-1) during sunrise and sunset.