You may remember Jesus' words in Scripture that we quote in the Eucharistic service: "Do this in remembrance of me." These words also play a prominent role in the Maundy Thursday liturgy, particularly the epistle reading from 1 Corinthians.
That idea of remembrance would have meant something different to the Disciples than it often does for us. Jesus isn't telling the Disciples to simply recall this event in their minds. He's telling them to remember in a way that makes the past event present for them now. That's how the Disciples would have celebrated Passover. Even though the Passover occurred long before their lifetimes, the Disciples would have celebrated the event as if they were a part of it too.
This idea of remembrance is why we celebrate the events of Holy Week when we do. Celebrating Maundy Thursday puts us into the timing of the Last Supper, a Passover/Pre-Passover meal. That's why we celebrate the service at night, so that we can better live into that moment.
Jesus would have be crucified the next day, thus we remember His death on Good Friday. Most churches hold a service at noon. This is because noon has long had a connection with the Crucification (see Hatchett, 134 and BCP 107). In Mark 15:33, the evangelist mentions a darkness covering the land at noon. Mark then sets 3PM for when Jesus died. There was a time when Good Friday was a three-hour preaching service from noon to three (see Alexander, 121), helping us to live into this period of time.
Even the Great Vigil of Easter has an important timing, this time for the Resurrection, which I have spoken about in more detail before. We hear in John 20:1-18 that it was still dark when Mary Madeline came to the tomb. Luke 24:1-12, the Gospel for the Vigil, has the timing at dawn, which means the Resurrection would have occurred before then at night, and it adds more meaning to our waiting in the Vigil, especially if our waiting lasts until dawn. For this reason, the Prayer Book says the Easter Vigil should be observed at a convenient time between sundown on Saturday and sunrise on Easter Sunday.
The timing of these services helps us to live into these moments of Jesus' Death and Resurrection. This is what Jesus is asking His Disciples to do when He tells them to "Do this in Remembrance of me."
But we actually do the act of remembrance each and every Sunday, which is why we say these words in the Eucharist. Every Eucharist lets us live into the events of the Death and Resurrection, making these events that go beyond time and space so that all of the Body of Christ can be present in them.