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.
KJV
 

Comments:

"I beseech you"
Means "I beg of you".  Even though Paul was an apostle who spoke with the authority of God and was inspired, his attitude towards others was one of submission.  What Paul was about to say, he said it with the air of man begging his readers to heed him. 

"brethren"
Paul was addressing brothers and sisters in Christ.  Let there be no doubt in the mind of the Bible student today that the readers of Paul's letter to the Romans were Christians in the body of Christ.  All of the commands, directives and exhortations contained within this letter are thus applicable to members of the Lord's body with an application for us today.   

"by the mercies of God"
Jesus died for our sins by the mercy of God.  Without that sacrifice on our behalf there would be no hope for any of us.  We learn from the Hebrews writer that the blood of bulls and goats can never take away sin (Hebrews 10:4).  The sacrifice of Jesus was the perfect sacrifice for all sin forever (Hebrews 10:12).  Without that sacrifice which came about by the mercy of God, it would not even be possible for us to do what Paul begs next.

"that ye present your bodies a living sacrifice"
The word bodies here is from the Greek word "soma" which means the physical body.  The living sacrifice we are to offer here is in contrast to the dead animal sacrifices of the Levitical system of worship.  Sacrifice was a way of life for those living under the old law.  A study of Leviticus begins with the observance of the free will daily burnt offering of the Israelites and from there moves into a host of sacrifices with many different purposes and on many different occasions.  What the Christian today needs to be aware of is the sheer volume of sacrifice that was a part of the daily lives of the Israelites.  What we can apply from that to us today is that with the death of Christ, the animal sacrifices passed from the lives of God's children.  The sacrifices of dead animals was replaced with the daily living sacrifice of our bodies.  The Israelites sacrificed dead animals.  Through the blood of Christ who was the one time perfect sacrifice for all sin forever, we today sacrifice ourselves in service in Christ's kingdom. 

The Sacrifices we make are ones of service to our fellow man as recorded in Matthew 25 and Hebrews 13:16.  In addition to this, our worship to God is called a sacrifice.  We offer the sacrifice of praise in song (Hebrews 13:15).  The offerings given by the Philippians to Paul were referred to as a well pleasing sacrifice to God in Philippians 4:18 and context.  We are begged by Paul to offer our bodies as living sacrifices as opposed to dead sacrifices.  The Christians life as a priest in Christ's kingdom is to be characterized by a lifetime of faithful service in sacrifice to God. 

"holy"
Strong's defines this word as "sacred (physically, pure, morally blameless or religious, ceremonially, consecrated)".  Our bodies offered in living sacrifices in service are consecrated which means set aside for service to God.  We were bought with a price, therefore we are not our own (1 Corinthians 6:19-20).  Our bodies are set aside for the glory of God and it is our responsibility to see to the fitness of our bodies for this service.

"acceptable unto God"
It would not be necessary to mention this if it were not possible for our sacrifice to be found unacceptable.  The responsibility for this is given to those being exhorted to offer their bodies as a living sacrifice.  The sacrifice must be acceptable to God.   

"which is your reasonable service"
Some modern translations render the word for "service" here as "worship".  This Greek word is "latreia" which is translated as "service" in every instance in the King James and the American Standard Version.  The Greek word for "worship" is "proskuneo".  There is a difference in the meanings of the words "latreia" and "proskuneo".   Service to God is not always worship.  Worship is done with God as the focal point and the sole object of one's adoration.  Service in God's kingdom does not have God as the sole object of one's attention and is therefore not worship.  Service is service and worship is worship.  The two are not the same. 

As for it being our reasonable service, by the grace of God, Jesus laid down His life for sinful man.  We didn't deserve it, we can't earn it, God was under no obligation whatsoever to offer us a means of redemption.  God could have left us to our fate and would have been perfectly justified in doing so.  yet, because of His love for us, He made the ultimate sacrifice for us, on our behalf.  God sent His only Son down here to be that sacrifice.  He sent the best He had, and the best He had died because of it.  And it was not a peaceful easy passing either.  Jesus Christ suffered at His death, naked, humiliated, shamed and spiked to a cross to bleed out and die.  So does it not stand to reason that we should give something back?  Is it not reasonable that we offer our bodies as living sacrifices in service back to the one who offered His dead body as a substitutionary punishment for what we should have received?   Jesus explained this in the parable of the unprofitable servant found in Luke 17.  The summary line of this parable gives us today the attitude we should have about our service to God in the kingdom of Christ:

Luke 17:10
Even so ye also, when ye shall have done all the things that are commanded you, say, We are unprofitable servants; we have done that which it was our duty to do.

He died for us and asked us to live for Him.  It's only our reasonable service.  Nothing for us to boast about, certainly not something that can repay the debt of gratitude we owe for it.  Jesus doesn't get to come down off the cross because of our service.  Even after all we can do, He still had to die for us and that is why our salvation is by God's grace.  There is nothing we could ever do to merit the opportunity we got for redemption.