The phrase "catch on" means to understand or become popular. There are numerous synonyms for this term, including comprehend, grasp, seize, fathom, apprehend, realize, and get the hang of. Other synonyms for "catch on" that reference popularity include become fashionable, take off, gain traction, and become a trend. These synonyms can be used interchangeably with "catch on" to add variety and nuance to your writing or conversation. By incorporating synonyms like these, you can convey your meaning more effectively and craft a message that will resonate with your audience.