Ultraviolet light from the sun dissociates 2H20 -> 2H2 + O2. Normally, the two species would quickly recombine, but with the low gravity, the hydrogen preferentially escapes the planet, and the oxygen oxidizes into the iron in the rocks. That's why its called the Red Planet.

If the O2 concentration in the atmosphere is high enough, the UV turns some of the oxygen to Ozone, 3O2 <-> 2O3. Note that that's a reaction that goes both ways, ozone is notoriously unstable. Some ozone converts back to oxygen, but the O3 concentration is now in equilibrium, forming a UV shield for the surface. But without lots of new oxygen being pumped continuously into the ionosphere this can't happen.

Ir would have happened here on earth, too, (although it would have taken much longer due to our higher gravity) but we have plenty of water and plenty of photosynthesis here to replace the O2.