Symbolic (or semiotic) analysis is the interpretation of signs and symbols, usually involving metaphors and analogies to both inanimate objects and characters in a film. Because symbols can have multiple meanings, you will need to determine what a particular symbol means both in the film and in a broader context, whether in other films, or in other disciplines, like literature.
Be sure to bring the analysis back to your thesis, or why this symbolism matters.
Some questions you could ask when writing a symbolic analysis essay: