This information is from a booklet called Celebrate Passover, Haggadah, A Christian Presentation of the Traditional Jewish Festival by Joan R. Lipis.
Haggadah means "the telling". Every activity during the meal is to remind (or tell) the people about God's many acts of kindness toward the people of Israel.
Bedikat Chametz (searching for leaven) The leaven signifies impure thoughts, words, or deeds which need to be removed from out hearts to worship God. It also reminds the people of the time they had to flee Egypt in a hurry and did not have time to wait for bread to rise.
Call to Worship sets apart this night as different from others.
Birkat Ha-Ner (Blessing Over the Candle) ushers in the new day and sanctifies the Seder. Intended to inspire the people to use their gifts for God.
Kaddesh (Sanctification of the Meal) The purging of leaven made the house holy and confession made each individual holy.
The Four Cups: Each cup reminds the people of the promises made by God in Exodus 6:6-7
Cup of Sanctification- "I will bring you out from under the yoke of the Egyptians."
Cup of Deliverance: "I will free you from being slaves to them."
Cup of Redemption:"I will redeem you with an outstretched arm and with mighty acts of judgment."
Cup of Praise: "I will take you as my own people."
Urchatz (Washing of the hands) In the days the temple was standing, it was part of the process of purification to be holy before the Lord.
Karpas (Eating the greens) Reminded the people of the hyssops used which applied blood to the door frames to protect the people.
Yachatz (Breaking the middle Matzoh) Some say the three pieces of Matzoh signified the priests, the Levites, and the congregation. Some say it represents the three patriarchs, Abraham, Isaac, and Jacob. Believers in Y'shua can say it represents Father, Son and Spirit. The middle Matzoh is broken. One piece is hidden from the children to be found later.
Maggid (Recounting the story of Exodus) Reminds the people of how God delivered them from Egypt.
Shulchan Orech (The table is spread) A long list of specific dietary laws were followed.
Tzaphun (Retrieving of the Afikoman, the Hidden Matzoh) The Matzoh was broken, hidden, and brought back. It signifies the Messiah was broken, hidden, and brought back to life.
Barech (Blessing of the Meal) Reminds the people of God's constant provision.
Hallel (Songs of Praise) Words of victory and surrender.
(My Spell Checker had a field day with this blog. Please excuse any misspelling that you find. I did the best I could.)