Jesus instituted the Lord's Supper on the night he was betrayed. Three of the gospel accounts record this. (Matthew 26:2629; Mark 14:22-25; Luke 22:17-20) According to Mathew, while Jesus celebrated the Passover meal with his disciples, he took bread, blessed it, broke it and gave it to the disciples. H said "take eat, this is my body".
Then he took his cup of wine, gave thanks, and gave it to them also. He said "Drink from it, al of you. For this is my blood of the new covenant which is see for many for the remission of sins".
Paul instructed the Corinthians in the matter in 1 Corinthians 11. After reciting the words of Jesus, Paul added "For as often as you eat this bread and drink this cup, you proclaim the Lord's death till he comes."
When we participate in the Lord's Supper, we acknowledge and give thanks for the atoning death of Jesus. He gave his body and his blood on the cross to pay the penalty for our sins. That work is finished. We believe he did it, we thank him for it and we proclaim that he did it through our participation.
The church will celebrate the Lord's Supper until the Lord returns. While we in the present acknowledge his death for us in the past, our continuing participation is a witness to our believe that he will return.