Why does dirty snow melt faster than clean snow?

Darker colours absorb heat from the sun better, "whiter" colours reflect it better... so dirty snow which is darker (even if it's only slightly) will absorb heat from the sun faster and better than clean white snow and therefore melt faster. You can see for yourself if you paint a piece of metal black and another white and leave them both out in the sunlight. The black piece will be significantly hotter than the white piece.