Planet Mars was named after the Roman God of war. In Astrology (the mass delusion that movement of planets far way, decides fate of men), the presence of the planet signifies danger. Red is equated with fear and hence, the planet has had considerable notoriety on Earth.
When it comes to human psychology, a lot of things are borne out of such symbolism. We know for sure today why Mars has a red color. That's because of advanced telescopes and space missions which have actually landed rovers on its surface and explored its soil.
We know that on Earth, any piece of iron, when it rusts, turns reddish in color. This conjecture of Mars being red because of rust was made, based on the similarity in color of rust and the observed color of the planet. It was validated after planet rovers like the 'Mars Pathfinder' actually examined the surface soil and made spectroscopic studies.
People agree that beauty is skin deep; so is Martian redness. That is, the redness of the Martian surface is only due to a thin layer of red ferric oxide dust (varying in thickness from some millimeters to as much as 2 meters deep) which covers the whole planet. This fact was revealed by rovers, as they dug up the Martian soil to make a geological study.
The redness of the soil is attributed to a combination of spectral properties of some minerals, which are related to iron. The color of any object depends on what it's made up of. Mars is reddish because the material, ferric oxide emits radiation in the red part of the visible electromagnetic spectrum.
The prime mineral whose radiative emission is responsible for the red color and which is present in the Martian surface dust is nanocrystalline red hematite (Alpha- Fe2O3). That is what has been revealed through the studies conducted by rovers that landed on the planet and orbiters which scanned its surface.
The next question which logically follows is, what process created so much of red dust on the planet surface. There are many theories regarding it, but none have been conclusively verified.
One theory says that Martian surface may have had water in the past, which caused the iron rust, while another recent theory proposes that the dust is the result of Martian atmosphere's interaction with the thousands of meteorites that collided with the surface.
There are many more theories. It may be a combination of all the suggested mechanisms or one of them. Only time and further investigation, combined with research, will reveal the truth.