"Saying Grace" is a religious tradition that spans most faiths. The idea is to give thanks to God for our food, and ask Him to bless it. In my LDS experience, few have called it "Saying Grace". To me, it has always been either "Bless the Food," or "Say the Prayer." I think I prefer "Saying Grace."
I did have a missionary companion who took the idea of "blessing the food" to a much more literal level than I had seen before. We would bow our heads at the table, and he would pronounce the blessing, which would be something like this: