This is about looking back on a past relationship and wanting your ex back - wanting to return to what you had. The first verse depicts how the writer is left behind. His ex has moved on but he hasn't and still hangs onto hope:  At first he is hanging onto hope but then he realizes that he must let go

 Fact:

Don Henley told the NME that he really did see a Deadhead sticker on a Cadillac.Henley says: "I was driving down the San Diego freeway and got passed by a $21,000 Cadillac Seville, the status symbol of the Right-wing upper-middle-class American bourgeoisie – all the guys with the blue blazers with the crests and the grey pants – and there was this Grateful Dead 'Deadhead' bumper sticker on it!"