We do this as it was an instruction from the Lord Jesus, the bread is a symbol of his body which was broken for us, the cup is a representation of his blood that was shed.
Below is an extract from the Gospel of Luke, Chapter 22 verses 19 and 20
And He took bread , and gave thanks, breake it, and gave unto them, saying "This is my body which is given for you; this do in remembrance of me." Likewise also the cup after supper, saying "This cup is the new testament in my blood, which is shed for you."