often means,

To give as a gift. Or, To set, place, or introduce into the presence, or before the face of a superior. (As, to'present' an ambassador to the king.)
Also, to offer; to exhibit.
Or, to put into the hands of another with ceremony.
(See Webster's 1828)

I beseech you therefore, brethren, by the mercies of God, that ye present your bodies a living sacrifice, holy, acceptable unto God, which is your reasonable service. And be not conformed to this world: but be ye transformed by the renewing of your mind, that ye may prove what is that good, and acceptable, and perfect, will of God.
Romans 12:1-2

To 'present your bodies a living sacrifice' means, to present your bodies as a living sacrifice to God; to give up sin for God's sake and keep your bodies acceptable and holy to Him