"This day must be commemorated by you, and you must keep it as a feast in Yahweh's honor." (Exodus 12: 14)
The Passover is a feast in Yahweh's honor. The Eucharist is the new Passover. Just as Yahweh instructed the Israelites to commemorate the Passover, so Christ instructed His disciples to celebrate the Eucharist in memory of Him. The Eucharist commemorates the passion, death and resurrection of Jesus.
When we eat "this bread and drink this cup", we commemorate the death of Christ until He comes again in glory.