Geulah, meaning redemption or deliverance, is what we celebrate on Pesach. On the last days of Pesach, we especially mark the redemption of Israel from the Egyptian armies at the Red Sea.
Literally gaal means to cover or protect (See Job 3:4). Galut, exile, the opposite of geulah, comes from the root meaning to uncover. Galut is the uncovering, or denuding, of the land of Israel of its inhabitants.
Geulah also refers to the ransoming or redeeming of property that used to be yours. The English word redemption also has this dual financial and spiritual meaning.
In the Pesach story, the redemption of Israel is Gods recovering of the Jewish people after they had been alienated, spiritually and physically, under Egyptian servitude. Physically, the Jews had been slaves to foreign rulers. Spiritually, many had fallen under the spell of idolatry. Geulah refers to liberation both from alien masters and from strange gods.
Among Jews who hope avidly for the messianic era, you often hear the wish expressed that we will all soon see the geulah shleimah, the complete redemption.
The messianic redemption in the future is understood to be the Pesach liberation from false tyrannies of the body and the spirit writ large (Talmud Berachot 13a.)