Read Romans 12:1-2.
God had shown them great compassion in giving His Son to die, in pardoning their sins, and this was the reason why they should devote themselves to God.
“That ye present”
The word used commonly symbolizes bringing and presenting an animal or other sacrifice before an altar.
It implies that it was a free and voluntary offering. Salvation is free; and the act of devoting ourselves to God is one of the most-free acts we could ever make.
The entire bodies of animals were offered as a sacrifice. Paul is saying the entire animal was devoted; and evidently meant the same for them to present yourselves, your entire person, to the service of God.
“A living sacrifice.”
A sacrifice is an offering made to God as atonement for sin; or any offering made to him and His service as an expression of thanksgiving and respect.
In other words, it implies that he who offers it presents it entirely, releases all claim or right to it, and leaves it in the hands and for the honour of God.
In the case of an animal, it was slain, and the blood offered. In the case of any other offering, such as the firstfruits, etc., it was set apart to the service of God; and he who offered it released all claims on it, and submitted it to God, to be used at His will.
This is the offering Paul beseeches them to make; that is to devote themselves to God, as if they no longer had any claim on themselves; to be used by him; to suffer and bear all that God might allow; and to give Him honor in any way He might require. This by the way is the nature of true faith and Christianity.