This is the song responsible for getting me into Leonard Cohen. I was very late to the game and should have been taken with him much, much sooner. The moment I heard the song and it clicked for me was while watching an episode to the short-lived series Karen Sisco*. As Cohen intimates in his intro in this video, this song is about his time in the famous Chelsea Hotel in the late 60s. As he usually dedicates the song to Janis Joplin, whether overt or furtive, the assumption is that the song is about her. The element of the story he tells in the intro in which he claims to be Kris Kristofferson is fucking hilarious.
*This, of course, was the series in which Carla Gugino took the reigns from Jennifer Lopez, who had played the filmic incarnation of Elmore Leonard's U.S. Marshal in Out of Sight, marking what might be the only instance in history in which the TV version of a character was hotter than the film version.
If you were looking for an entry point to a Leonard Cohen obsession, this song and (in a larger sense) New Skin for the Old Ceremony is your gateway. Also, do not hesitate to try to track down the 2005 Liam Lunson documentary Leonard Cohen: I'm Your Man, which offers a ton of insight from the man himself along with a lot of performances and is available on DVD through Netflix.