What is the meaning of [Fight the good fight]

An evangelical call to believe in and spread the Christian faith.

The words are from the Bible, Timothy 6.12 (King James Version):

Fight the good fight of faith, lay hold on eternal life, whereunto thou art also called, and hast professed a good profession before many witnesses.

The phrase was commonly used in both the UK and the USA in the 19th century, when those using it would have been well versed in Biblical texts. In November 1843, the Gettysburg newspaper The Republican Compiler printed what it claimed to be a verbatim report of a speech made to Republican forces by the Reverend Joab Prout, on the eve of the Battle of Brandywine:

“Soldiers – tomorrow morning we will go forth to battle … your unworthy minister will march with you, invoking God’s aid in the fight … need I exhort you to fight the good fight for your homesteads, and for your wives and children!”