While My Guitar Gently Weeps is a track originally written by George Harrison and recorded by The Beatles, included on their 1968 album The Beatles, more commonly known as "The White Album" (in the same way Prince's untitled 1987 album became known as "The Black Album").
A live version by Tom Petty, Jeff Lynne, Steve Winwood, Dhani Harrison and Prince, recorded on 15 March 2004, was broadcast during the 2004 Rock And Roll Hall of Fame induction ceremony, and in 2009 was included on both a 3 DVD set and a 9 DVD set both titled Rock And Roll Hall Of Fame + Museum: Live (a slightly different mix of the video, with Prince's guitar lower in the mix, is streamed on www.georgeharrison.com).
An audio version of the track was released on the 2011 digital album The Best Of Rock And Roll Hall Of Fame + Museum Live, released exactly seven years to the day after the performance itself. The performance came at the end of the show in which both Prince and George Harrison (posthumously) were inducted into the Hall of Fame; the show is traditionally capped off with an all-star jam, and this track, mostly performed by George Harrison's friends (and his son, Dhani Harrison) acted as a tribute to Harrison while also showcasing Prince as an inductee.
Prince has not performed this song at any other point, and is not known to have recorded a studio version.
Of note is that this is the earliest performance by Prince of a song by The Beatles; he has since performed Come Together, The Long And Winding Road and With A Little Help From My Friends (Prince had also worked on a studio cover version of Day Tripper for the unreleased Flash album), although While My Guitar Gently Weeps is the only George Harrison-written track he has performed.