He was on the verge of suicide. He saw nothing to live for and was prepared to end it all right there. You may not be on the verge of suicide. But, if you have never trusted the Lord Jesus Christ and been saved from your sins, you know something of a hopeless life. We cannot save ourselves.
Human works are futile to produce genuine righteousness.
For there is no other name under heaven given to men by which we must be saved. The jailer had repented. His attitude and question to Paul were proof of that. He came as a broken, trembling, repentant man and asked the way of salvation. Faith is committing yourself to the Lord Jesus.