Redemption is one of the central themes of the Bible. God redeemed Israel from Egypt (Ex 12), Messiah is both a ruler and redeemer (Acts 7.35), Messiah gave himself to redeem us from lawlessness (Titus 2:14), etc. The word 'redeem' means to pay for and take posession of something. For example, if you drop your trousers off at the cleaners, you can redeem them by paying the cleaning bill and then picking them up. The payment, while necessary, does not complete the redemption. That requires taking posession.
It is important to note that redemption requires ownership. I would be wrong if I tried to redeem your trousers; they don't belong to me. The meaning of the word doesn't change when it applies to God. He only redeems what belongs to Him. So to understand the subject of redemption, we must first understand ownership.
The essence of the dispute between God and Pharaoh was the question of who owned Israel. Pharaoh asserted that they were slaves and hence his property. God disagreed and proceeded to redeem what was His. So given that the ability to redeem depends on ownership, how did we get to the place where our ownership is in dispute?
The answer, of course, goes back to the garden. We were created to be God's interface into the created world. We were designed to operate both in the realm of the spirit and in the physical. We walked with God and looked to Him to determine good from bad. The serpent convinced Eve that God, by withholding the fruit of the tree, was preventing her from reaching her potential. She ate, becoming her own authority for determining good from bad, and transferring ownership from God to the world.