Exagorazo (ἐξαγοράζω) is a compound of ek (out of) and agorazo (to buy in the marketplace). It means to buy out of — specifically to redeem someone from slavery, legal condemnation, or the curse of the law by paying the purchase price. Paul uses this word in two of his most important redemption texts: Galatians 3:13 ('Christ redeemed [exagorazo] us from the curse of the law') and Galatians 4:5 ('to redeem [exagorazo] those under the law, that we might receive adoption').
The marketplace (agora) background of exagorazo is theologically rich. In the Roman world, slaves could be purchased in the agora and then freed. To say Christ exagorazo-ed us is to say he entered the slave market of sin and paid the price — not to own us as a different master, but to bring us into adoption as sons (Galatians 4:5). The price paid was his own blood (1 Peter 1:18-19). Ephesians 5:16 and Colossians 4:5 use exagorazo in the ethical sense of 'making the most of' or 'buying back' time — applying the redemption metaphor to daily life.