I really like this piece. It's two works of Dalí's that I really enjoy more than the others (although, he is one of my favorite painters in general).
The woman figure is alone in the foreground, which is typical of art I like. Although this is a surrealist work, the is a realistic figure (not like Cubism, which takes away the figure-part). The drawers can have symbolism any which way you like it: her thoughts, her inner spaces, how compartmentalized she is, that they're open to the world, that they're empty...could be anything.
There is a city in the background full of normal figures, as well as another drawer-person and disembodied drawers, indicating another class of people or some accoutrement that, when applied to people, transforms them into a different sort. Of course, that's only if you think that's it is reasonable to apply any sort of meaning or analysis to surrealist art.
I must say, though, nice knobs.