Excerpts from Books and Wikipedia
"When asked about the song's meaning during a December 1980 interview with David Sheff for Playboy magazine, Lennon told Sheff that Dick Gregory had given Ono and him a Christian prayer book, which inspired him the concept behind "Imagine". The concept of positive prayer ... If you can imagine a world at peace, with no denominations of religion – not without religion but without this my God-is-bigger-than-your-God thing – then it can be true ... the World Church called me once and asked, "Can we use the lyrics to 'Imagine' and just change it to 'Imagine one religion'?" That showed [me] they didn't understand it at all. It would defeat the whole purpose of the song, the whole idea." [Wikipedia] In the documentary "John & Yoko: Above Us Only Sky," Yoko says that she believes that the whole purpose of her meeting and marrying John was to make this song.