Paul McCartney wrote this about his travel adventures with his wife Linda. When The Beatles were breaking up, it took on new meaning as a gesture of affection from Paul to John Lennon.
Lennon and McCartney sang together on this song, which is something they did a lot in the early years of The Beatles, but not so much later on, when they started writing separately and restricting the lead vocal to whoever wrote the song.
This song is mostly acoustic, with Lennon and McCartney each playing acoustic guitar. George Harrison's electric guitar is there, but low in the mix. There is no bass on the track.
This appears twice in the Beatles documentary movie Let It Be, first as a duet by John and Paul and then with the whole band.
John Lennon did the whistling on the fade-out.
John Lennon often amused himself (and others) in the studio with off-kilter banter before takes, and occasionally parts of these would be included on the tracks. "Two Of Us" starts with one such rant, where he says: "'I Dig A Pygmy' by Charles Hawtry and the Deaf Aids, phase one in which Doris gets her oats."
VH1 used the title for a fictional movie in 2000 about Lennon and McCartney getting together in the '70s. This was the first original movie VH1 made. Others they produced include films about Meat Loaf and Def Leppard.
Other notable songs McCartney wrote for/about Linda: "My Love," "Maybe I'm Amazed," "Calico Skies," "Warm & Beautiful," "Golden Earth Girl," "Some days," "She's My Baby," "Long Haired Lady," and "The Lovely Linda."