資料が届いたようですので、事務室に取りに行ってまいります。 "Because it looks like the documents have arrived, I go to the office to fetch them."
This sentence is an example from the grammar section of my textbook. I've encountered this 行ってまいります only once before (at least as far as I can remember), and I couldn't beat much sense into it. When I search for まいります/まいる on jisho, I find nothing. I can search for 行ってまいります and find this http://jisho.org/search/ittemairimasu . But since the result is a set phrase which has a meaning which doesn't even apply in this case here, it doesn't help much.