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You are most likely to come across this expression or, rather, a phrasal verb, in some kind of an exam-related situation. If you are a student and have to write essays, there will be certain things you’ll be marked down for. The same goes for driving tests (forgive yet another reference to my driving experience).
As you’ve probably guessed, to mark down means ‘to give a student a lower mark for their work for a particular reason’. However, this phrasal verb has some other meanings, that you can look up here.
Some examples of how it’s used:
– The criteria are “restaurant chains, bars/coffee houses, motor dealerships, hotel & spa chains, supermarket chains, clothing and shoes, toiletries and cosmetic chains, schools, leisure, entertainment”. You get marked down for fast food outlets, betting shops and “value” supermarkets. (The Guardian).
– If a school isn’t following an optional policy, it gets marked down in the report in the same way as if it were failing in a statutory requirement (The Guardian).
Confessions of the Linguistic Spy 