The Last Supper refers to the last meal between Jesus and his apostles, which was held just prior to his death. This meal was a Seder or Passover meal, since all participants were Jewish. The time of the supper was that of the feast commemorating the "passing over" of the Angel of Death in Egypt, just prior to the Exodus from Egypt.
In the process of the last supper, Jesus told his disciples, "Do this in remembrance of me." This command was understood by the early Christians as a command to recreate the Last Supper in a remembrance service.
Initially, the remembrance service took the form of agape feasts. Agape is one of the Greek words for love. This service apparently was a full meal, with each participant bringing their own food, with the meal eaten in a common room. Some echoes of this meal remain in fellowship or potluck dinners held at some churches.
This service is known as the Eucharist in Catholic traditions. The name Eucharist is from the Greek word eucharios which means thanksgiving or thank you. Catholics typically restrict the term 'communion' to the distribution to the commmunicants during the service of the body and blood of Christ.