Answer:
The Persistence of Memory is considered an important example of surrealism because it examines the subconscious world and delves into human psychology. Some viewers make claims that it alludes to some technilogical advances of the time period. According to some analysts, the appearance of the clocks and watches refer to both time and mortality, two very philosophical ideas at heart.
On another note, because the painting is in a dream-like state, the clocks might be considered melting away because they have no impact on you in your own mind. Art history scholars counter that the melting clocks relate to Albert Einstein's Theory of Relativity.
No matter what it truly was intended to mean though, it remains an iconic piece of surreal art to this day.