Christians who affirm their renewed and strengthened commitment to their religion are called 'born again'. To be born again is to be 'born of the spirit'; the first birth being the physical birth of the flesh.
From the Bible, John 3.3 (King James Version):
Jesus answered and said ... Except a man be born again, he cannot see the kingdom of God.
The term began to be used in the 1960s to give a specific name to those who renewed their faith. The earliest printed reference I can find to 'born again' in this sense is from the Reno Evening Gazette, October 1914:
"It [Christian Science] gives man the opportunity of being born again."
The first that specifically mentions 'born again Christians' is the Decatur Evening Herald (Illinois), December 1928:
"I knew I had the new desires that a born-again Christian acquires."
By the 1980s the term was well enough established in the language for it to begin appearing in modified forms in jokes (always a good measure of linguistic acceptance). In 1981, at the start of the Wimbledon Tennis Tournament, and after Bjorn Borg had won five consecutive titles there, The Times published an article assessing his chances with the headline 'Bjorn Again?'. Since then an Abba tribute band has also adopted 'Bjorn Again' as their name.
See other phrases that were coined in the USA.