Deer apples are the drop apples that may sit on the ground for a day or two, and are sometimes a bit green. They are usually bruised in one spot and sometimes rotten/moldy. But, 75% of the apple is perfectly usable. Just need to cut out the bruises and that will tell you if you have an apple that you should throw away (or give to the animals). They're great for pies and applesauce.
I recently moved up to "seconds" which are the picked apples that are less than perfect, usually some kind of cosmetic blemish. Deer apples are about $8 per bushel (about 40#), seconds are $12 a bushel and the perfect apples are $20-24 a bushel.
They are called deer apples because some folks put a big pile of apples in the woods to bait deer. It is illegal to do this in NY, although some folks will put a pile out before deer season, then remove it a couple of days before opening day.