The reason red meat is colored that way (as distinct from white meat) is because the muscle tissue contains a significantly higher concentration of myoglobin and, to a lesser degree, hemoglobin. These two proteins also cause certain parts of chicken and turkey to be colored darker than others.
Myoglobin and hemoglobin contain an atom of ferrous iron which binds to oxygen, allowing the tissue to absorb oxygen from the bloodstream. When the animal is slaughtered and the meat is cut, oxygen is absorbed by the iron atom and the meat turns red.
The concentration of myoglobin has nothing to do with the high cholesterol content usually associated with red meat. In fact, ostrich meat, which is red despite the fact that it's technically poultry, is very low in cholesterol.