There are very few ordinances required under the New Covenant. Baptism, laying on of hands, anointing with oil and the breaking of bread in communion are about all that are established in the New Covenant. Each of these is important, and especially the breaking of bread in communion for it is a remembrance of all the Jesus did for us.
On the night that the Lord was betrayed he took bread, blessed and broke it, and gave it to the disciples to eat. He said to them, “Take, eat; this is my body.” (Verse 26) He then took the cup and after giving thanks gave it to the disciples to drink saying, “Drink of it, all of you; for this is my blood of the covenant, which is poured out for many for the forgiveness of sins.” (Verse 27-28)
The symbolism in these acts and what they mean to us today cannot be understated. Both of these actions in the breaking of bread and the drinking of wine in communion are symbolic and meant to remind us of the sacrifice the Lord made for us on our behalf. It was through his sacrifice that we could be set free from sin, set free from the law and have the freedom to live in Jesus Christ. It is only through this freedom that we can then be transformed into the image of Christ and be prepared to be able to live a life in perfection with Jesus and the Father. Without the sacrifice Jesus made none of this would be possible. So it is important that we remember what he has done for us in this way.
As for the symbolism we should consider the bread and the cup as Jesus described them. The bread is representative of his body, which was broken for us. His body was the sacrifice made for us so that we would be set free. As the lamb was sacrificed each year as a sin offering for the people of physical Israel, Jesus became the sin offering for the people of the spiritual Israel. And more than that, the lamb was offered annually for the sins of the people because that sin offering could not make a man perfect. But Jesus as the Lamb of God who was the perfect offering needed to be offered only once, for in his offering the ability to be made perfect was achieved.
Under the Old Covenant the offerings were made to address the weaknesses of man, and because man was weak the offerings had to be made continually. But in Christ the offering is made just once for in Jesus we have the ability to reach perfection through the working of the New Covenant and the transforming power of the Holy Spirit. By separating man from sin and setting him free from the law so that sin no longer has power over man, Jesus brought us to a place where there is no condemnation. How can you be in condemnation when the Lord has forgiven your sin, set you free from sin and removed you from the law that defines sin for what it is? If all of these things have occurred then you no longer have the condemnation of sin hanging over your head and you have perfection by faith. But in this state where there is no sin, the Lord has then given us the Holy Spirit to change us gradually into his image so that the perfection we have by faith can be completed and we can become perfect, as he is perfect.
The cup that we drink in communion with the Lord is a remembrance that he shed his blood for us. In order to ordain the New Covenant blood had to be shed, just as the Old Covenant was ordained through the shedding of the blood of animals. The blood was brought into the temple and offered for the cleansing of the people from their sin and also to ratify the covenant. In the same way Jesus has taken his perfect blood into the presence of God and offered it so that those who come to God through Jesus Christ are cleansed and his blood ratifies the covenant and brings the New Covenant into force.
The power and the wonder of this process are simply mind-boggling. What the Lord has done for us to give us life is astounding. Thus we remember his sacrifice and the giving of his body and blood so that we may have life when we come together in the breaking of bread in communion. There is much more that can be said to describe how this whole process was set up and how it works, which you can find in my free eBook on the Foundations of Christianity.