Then he brought them up into his house and set food before them. And he rejoiced along with his entire household that he had believed in God.
The account of the conversion of the Philippian jailer is a story worth analyzing to see just how the gospel works. The details are simple and direct. Paul and Silas had been mobbed, beaten, and thrown in prison by an outraged Philippian pagan mob. The jailer was under strict orders to keep them secure, so once they were confined in stocks in the inner prison, he thought that he had done his duty for maximum security.
But Paul and Silas keep worshiping God by singing praises, and as the entire prison listens, God interrupts with deliverance in an earthquake that opens prison doors and unfastened every chain. The jailer's ability to ensure maximum security is gone, and confused, he is ready to fall on his sword in shame. Paul calls out to him to reassure him no one is escaping (a minor miracle no doubt brought about by a change of heart among the prisoners, perhaps by listening to Paul and Silas confidently worship God).
It is at that moment of clarity that the jailer himself wants salvation and finds freedom. The gospel is given to him as his only hope (Acts 16:31). From there Paul and Silas shared the Word with all in the jailer's household. They believed, cared for Paul and Silas (ironically keeping them safe through hospitality rather than imprisonment), and rejoiced in their new found salvation. God moved, their need for Jesus was realized, the gospel was clear to them, they believed and were saved. What a beautiful, clear picture of how the gospel works!