The bread and the wine are symbols of the body and blood of Jesus. When Jesus spoke these words, he had not yet been sacrificed. Luke 22:19-20:
And he took bread, and when he had given thanks, he broke it and gave it to them, saying, “This is my body, which is given for you. Do this in remembrance of me.” (20) And likewise the cup after they had eaten, saying, “This cup that is poured out for you is the new covenant in my blood.
The bread Jesus was breaking here, wasn’t his literal body – he had yet to be hung on the cross. It represented what he was going to do. The same for the wine he gave them – his blood hadn’t yet been shed, but the wine represented the blood that would be shed. These words were not meant to be taken in a literal sense then, nor are they now.
Consider the incident when Jesus warned his disciples of the leaven of the Pharisees and Sadducees. Jesus said “Watch and beware of the leaven of the Pharisees and Sadducees.” The disciples were puzzled and thought Jesus said this because they brought no bread. Jesus then said to them (Matthew 16:8-12):
“O you of little faith, why are you discussing among yourselves the fact that you have no bread? … How is it that you fail to understand that I did not speak about bread? Beware of the leaven of the Pharisees and Sadducees.” (12) Then they understood that he did not tell them to beware of the leaven of bread, but of the teaching of the Pharisees and Sadducees.
Jesus was using the leaven as a symbol of the teaching of the Pharisees and Sadducees. In a similar way, Jesus is using the bread as a symbol of his body and the wine as a symbol of his blood. This institution is to help us graphically remember the sacrifice he made for us and the implications this sacrifice should have for us.
Paul, speaking of the bread and wine says in 1 Corinthians 10:16-17:
The cup of blessing that we bless, is it not a participation in the blood of Christ? The bread that we break, is it not a participation in the body of Christ? (17) Because there is one bread, we who are many are one body, for we all partake of the one bread.
Paul doesn’t speak of the wine miraculously becoming the blood of Christ and the bread miraculously becoming the body of Christ. But he does speak of the symbology of our taking the wine and the bread as representing our unity with one another and with us being involved with the sacrifice of Christ. As Jesus said in Matthew 10:38 “whoever does not take his cross and follow me is not worthy of me” and Paul in Romans 6:5-13
For if we have been united with him in a death like his, we shall certainly be united with him in a resurrection like his. (6) We know that our old self was crucified with him in order that the body of sin might be brought to nothing, so that we would no longer be enslaved to sin. (7) For one who has died has been set free from sin. (8) Now if we have died with Christ, we believe that we will also live with him. (9) We know that Christ, being raised from the dead, will never die again; death no longer has dominion over him. (10) For the death he died he died to sin, once for all, but the life he lives he lives to God. (11) So you also must consider yourselves dead to sin and alive to God in Christ Jesus. (12) Let not sin therefore reign in your mortal body, to make you obey its passions. (13) Do not present your members to sin as instruments for unrighteousness, but present yourselves to God as those who have been brought from death to life, and your members to God as instruments for righteousness.