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
(see Webster's 
I beseech you therefore, brethren,
by the mercies of God,
that you 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.

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.