The moon appears orange when the sunlight it reflects passes through a thicker portion of the Earth's atmosphere. Generally, the moon only appears orange when it is close to the horizon.
The colors of the sky occur because of the scattering of white light by Earth's atmosphere. The blue of a clear daytime sky is due to Rayleigh scattering, a wavelength-dependent scattering of light that disperses shorter, bluer waves more strongly than longer, red wavelengths. Near the horizon the atmosphere is thicker, and the shorter wavelengths scatter in all directions, away from they eyes of onlookers, leaving longer orange and red wavelengths more visible.
The moon is luminous because it reflects light from the sun, so the same principles that cause orange sunsets also cause the moon to appear orange near the horizon. As the moon rises higher in the sky, the orange fades to bright white. Residents of cities and industrial areas view redder sunsets and a deeper orange moon because of the additional particles in the atmosphere due to pollution.
During a full lunar eclipse, the moon appears red when the eclipse reaches its peak, or totality. At totality, the sunlight reaching the moon passes through a swathe of thick air, much like during sunset, causing an orange or blood-red moon. If there were no atmosphere, the moon would appear to vanish completely during totality.