These are a pair of concepts that tend to hound beginning writers, especially beginning writers who come from an academic environment. This is largely due to the fact, I think, that a lot of higher education, even of writers, is less about writing than it is about reading. Colleges spend a lot more time on analysis of fiction than it does on its creation, after all it’s a lot easier to teach in a systematic fashion. But the tools one brings to bear in understanding what someone has written are much different than what you use to write something. Theme and symbolism are two such tools. Wielding these twin swords, a talented person can take a novel and dissect it like a chef at a Japanese steakhouse, leading to all sorts of insights. . . But you need to remember something, that as a writer in this instance you’re not the chef, you’re the cow.
I’m not saying ignore these high level concepts. I am saying that both are largely emergent properties of human psychology and narrative. Both are simply shorthand ways people use to talk about what the author (or the text, or the reader, depending on the critic’s schools of thought) meant. So since it is impossible to write something linguistically comprehensible and devoid of meaning (despite the best effort of politicians to prove otherwise) all narrative by definition has some level of theme or symbolism involved. So if you’re fired up to write something, don’t waste a lot of time trying to shoehorn a theme into it, it’s already there.
(The best example of the idea of theme and symbolism being eergent properties is the surrealist film Un Chien Andalou which very pointedly supposedly had no narrative or symbolic meaning at all. Bunuel and Dali tried to simply capture image after image of irrational dreamlike intensity. Even so, it is almost impossible to watch without imposing some narrative structure and meaning to the images.)