Lennon began writing the song in the Fall of 1966, while in Spain filming Richard Lester's How I Won The War.
The song expressed for Lennon a nostalgic look back at the Salvation Army orphanage in Woolton, which was called Strawberry Field. Lennon and his childhood friends Pete Shotton and Ivan Vaughan used to play in the trees behind the orphanage.
The released version of the song is actually an edit of two different performances. Lennon liked the first minute of take 7, and the ending of take 26, so producer George Martin edited the two takes together. The only problem was that both takes were played in different keys and at different tempos. So, one take had to be sped up slightly, and the other had to be slowed down. The edit is subtle but detectable, exactly 1 minute into the released version. (Although - just to nitpick - CD counters may give the exact time as 0:59.)
The instrument used for the flute-like sound in the song's opening is a Mellotron synthesiser, which used eight second tapes of real instruments for each key.
Contrary to belief of the Paul Is Dead hoax supporters, Lennon is actually saying "Cranberry Sauce" at the end of the song and not "I buried Paul".
The song, which was the first to be recorded during the Sgt. Pepper's Lonely Hearts Club Band sessions made it to number two on the British charts, although it could have easily been a number one single. Unfortunately for the Beatles, it was released, backed with "Penny Lane", on a "double A sided" single, which meant that both the sales and airplay statistics were split between the two songs, instead of being recorded collectively. The number one single at the time was Engelbert Humperdinck's "Release Me".
The promotional film for the song, featuring (among other things) the Beatles pouring paint over an upright piano, was shot in Knole Park in Sevenoaks. The exact location is fairly easy to find, being on one of the main roads through the park with a recognisable tree.
External link
Alan Pollack's notes on Strawberry Fields Forever:
http://www.recmusicbeatles.com/public/files/awp/sff.html