The author of Romans apostle Paul is making an appeal to all believers in Jesus Christ to worship God. The idea here is to consider what God has done for you. When God wanted to save mankind He gave everything He had precious to Him. God gave us His only begotten Son, Jesus Christ. There was nothing more precious God could have given. When Jesus came, He gave Himself for us. He did not hold back anything. He is the greatest gift mankind ever has and will get. Jesus presented His body to take the punishment for our sin and He did. Because of such a sacrifice, it brought an end to all other sacrifices and the spilling of blood.
The reciprocal thing a believer can do is to present all the members of his body and faculties as an offering to God. Since we are alive our presentation is described as a living sacrifice. Just as He is holy we are also required to be holy. 1Pet. 1:16 “because it is written, "Be holy, for I am holy.". All members of our body have to be brought under control. This is a done rationally and intelligently as a spiritual worship.