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You’re So Vain

The song is a critical profile of a self-absorbed lover about whom Simon asserts “You’re so vain, you probably think this song is about you.”

The title subject’s identity has long been a matter of speculation, with Simon stating that the song refers to three men, only one of whom she has named publicly, actor Warren Beatty.[5]

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Mick Jagger contributed uncredited backing vocals for the song. When asked how this collaboration occurred, [Carly] Simon said:

“He happened to call at the studio. ... I said “We’re doing some backup vocals on a song of mine, why don’t you come down and sing with us?”[32]
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References in the song

Gavotte—used in the line “You had one eye in the mirror as you watched yourself gavotte”—is a French dance. In this context it can be taken to mean moving in a pretentious manner.[33]

Simon said the line “clouds in my coffee” came “from an airplane flight that I took with Billy Mernit, who was my friend and piano player at the time. As I got my coffee, there were clouds outside the window of the airplane and you could see the reflection in the cup of coffee. Billy said to me, ‘Look at the clouds in your coffee’.”[34]

The line “I hear you went up to Saratoga and your horse naturally won” refers to the Saratoga Race Course horse-racing season held in late July, August, and early September in Saratoga Springs, New York. The season is frequented by the rich and famous of New York and other East Coast cities.[35]

The line “Then you flew your Learjet up to Nova Scotia to see the total eclipse of the sun” could refer to either of two solar eclipses visible from Nova Scotia in the early 1970s, on March 7, 1970,[36] and July 10, 1972.[37]

https://en.wikipedia.org/wiki/You%27re_So_Vain#References_in_the_song