When Ezra leads the people in publicly confessing their sins, the Israelites refer to the Exodus as a symbol of God's love and mercy toward his people, and also as an example of the people's tendency toward disobedience (dancing around that golden calf, etc.) He says:
And you saw the distress of our ancestors in Egypt and heard their cry at the Red Sea. You performed signs and wonders against Pharaoh and all his servants and all the people of his land, for you knew that they acted insolently against our ancestors. You made a name for yourself, which remains to this day. And you divided the sea before them, so that they passed through the sea on dry land, but you threw their pursuers into the depths, like a stone into mighty waters. Moreover, you led them by day with a pillar of cloud, and by night with a pillar of fire, to give them light on the way in which they should go. (NRSV Nehemiah 9:9-12)
Ezra wants God to do the same thing today—to lead his people out of slavery. He believes that they still are slaves dominated by foreign powers, even if those are relatively benevolent foreign powers like the Persian Emperors. The Exodus becomes a symbol for their current situation.
This symbolism becomes most clear when the people celebrate the Passover for the first time since being freed from exile (Ezra 6:19-22). They've escaped from Babylon like they escaped from Egypt, so they celebrate the same way.