I thought a mosquito bit the back of my leg and when I went to check it out it looked like a huge nasty bruise. What is it?

Ecchymosis. It could still have been a mosquito bite that punctured a small vein or capillary and caused some bleeding. If there is surrounding redness and warmth, an infection may be present and an examination by your physician is needed.
Hard to say. Lots of things can bite and leave a bruise. Without more info I cant be of much help.