1. Pesach is the festival celebrating the birth of the people of Israel.
2. Pesach has a nationalistic aspect: And you are the ones God took and brought out of the iron furnace, out of Egypt, to be his people of heritage (Deuteronomy 4:20).
3. The Pesach sacrifice is both an individual offering and a communal one. It is brought by a group and eaten in a group. There is no-one alone on the Seder Night - whoever is in need can come and join in the Pesach.
4. On Pesach the Hallel is not said in full except on the first (and in the Diaspora also the second) day, because of 'do not be happy when your enemy falls !'
5. The rabbis saw the seven days of Pesach as corresponding to the seven days of Creation. (Midrash Exodus Rabba, section on Bo)
Two reasons given for the Sabbath in the Ten commandments:
because God created Heaven and Earth ... in six days and rested on the seventh, therefore ... (Exodus 20:8-11).
you are to remember that you were a slave in Egypt and GOD brought you out ... therefore GOD ... commanded you to observe the Sabbath (Deuteronomy 5:13-15).
6. Pesach is the New Year for the Pilgrim Festivals.
7. On Pesach God interfered in man's affairs. He 'went down' to rescue Israel. I have seen my people's suffering ... and I have come down to rescue them (Exodus 3:7-8).
8. The central mitsvah of the festival is that of matsah.
9. Pesach is celebrated in the month of the barley harvest ('ripe barley') in which we left Egypt. God dealt kindly with Israel in choosing this month for Israel, when it was neither too hot, nor too cold, not too wet to travel. (See Rashi on Exodus 13:4.)