What does the 'Persistence of Memory' mean?

I have a book on surrealism that specific talke about this painting. In short the painting is about Dali's subconcious fear of death, which I will further explain with a small exert from the book:

The painter's portrait (which is the weird snail like thing in the foreground) resembles a snail creeping along the ground. The indicators of time are what form the real subject of the painting though. These indicators or clocks undergo a far-reaching transformation almost impossible to grasp through the use of logic. It is not the forward movement of the watch hands but the melting of the watches themselves that show time slipping away. The clock with ants and the tree with no leaves are premonitions of approaching death. Do these imitations of mortality refer to the lifeless head and liquefying body of the painter lying on the ground? Is the picture about his unconsious fear of death or the Persistance of Memory that parayses him?

And if you are interested, the book I found this in is called: Surrealism by Cathrin Klingsohr-Leroy. It has more artists then Dali in it, but it is really a great book, in my opinion.