"to take my Grade A loins off" (Phoebe said it on Friends. Full sentence: But, you know, am I ready to take my Grade A loins off the meat market?)
"My grade-A loins" here refers to her upper legs, which she is claiming are very attractive.
The sentence as a whole means "I am going to stop looking for dates/partners". Or more literally "I am going to stop offering my good-looking body to attract dates."
There is a bit of word play here. "meat market" means a singles bar or other venue in which people are looking for dates or sexual encounters. But it also means a place where actual meat is on sale, a butcher's market. (The singles sense is derived by metaphor from the older sense.) "loin" means a part of a person's body, but also a particular cut of meat ("loin of pork", for example). So the statement is playing on the notion of a "meat market" being a place where people offer themselves as if they were meat to be cooked and eaten.
The use of "grade-A" contributes to this same word play, because while it means "of very good quality" in general, it is very specifically and commonly used in rating meat for sale, as in "grade-A steak".
I should mention that "off the market" and particularly "take X off the market" is a fixed phrase meaning "stop offering for sale" or by metaphor, "stop making generally available". Therefor the phrase isn't "take my grade-A loins off" but "take X off the market" where X is "my grade-A loins".