prisoner: a person held in custody, bound or under guard.
The word names a person who is bound: someone held in custody, often literally in chains. In the Gospels it is Barabbas, the notable prisoner the crowd wants released. In Acts it is Paul in Roman hands, along with the other captives held beside him, and in the letter to the Hebrews it is the believers in jail whom the church is told to remember and support.
Paul then takes this same ordinary word and gives it a striking twist. Writing from a Roman cell, he calls himself not Rome's prisoner but the prisoner of Christ Jesus. He is bound in fact, yet he insists that the one who truly holds him is the Lord he serves, not the empire that jailed him.
Greek has close neighbors for this idea: δεσμώτης, another word for a person held under guard, and αἰχμάλωτος, a captive taken in war and led away. This word keeps the focus on being bound.