What do we call when one thing symbolizes another in text, as in the phrase "it's raining cats and dogs"?

The correct term for when one thing symbolizes another in a text is a metaphor. A metaphor is a figure of speech that directly compares one thing to another for rhetorical effect, suggesting that one thing is another, without using "like" or "as," which distinguishes it from a simile. The phrase "it's raining cats and dogs" exemplifies a metaphor by comparing heavy rain to an absurd scenario of animals falling from the sky, thus conveying the intensity of the downpour rather than describing it literally.

In this case, the term "simile" refers to comparisons using "like" or "as," which does not apply to the phrase in question. Personification involves attributing human characteristics to non-human entities, which is not relevant here. Symbolism, while similar, refers to the use of symbols to signify ideas and qualities beyond their literal sense, making it less applicable to the specific phrasing of the metaphor given in the question.