It is an apology type of excuse me. Pardon is used to get through. If I remember correctly, afedersin comes from the turkish word meaning forgive, so it means forgive me. I think, I'm no turkish expert.
Basically "I do". But it's used a lot together with nouns to turn them into verbs -- e.g. teşekkür ederim "I do thanks/thanking", but a better translation is just "I thank" or "thank you".