I have fought a good fight - The Christian life is often represented as a conflict, or warfare; see the notes on 1 Timothy 6:12. That noble conflict with sin, the world, the flesh, and the devil, Paul now says he had been able to maintain.
I have finished my course - The Christian life, too, is often represented as a “race” to be run; compare the notes at 1 Corinthians 9:24-26.
I have kept the faith - I have steadfastly maintained the faith of the gospel; or, have lived a life of fidelity to my Master. Probably the expression means that he had kept his plighted faith to the Redeemer, or had spent a life in faithfully endeavoring to serve his Lord.