proverbial
Very well-known or often repeated, like a famous saying.
Proverbial describes something so well-known or often repeated that it has become like a proverb: a familiar saying everyone knows. When something is proverbial, it's the standard example people use over and over.
If your teacher warns that you're skating on thin ice with your behavior, that thin ice is proverbial. It's not real ice, but everyone understands the image because the phrase is so familiar. When someone says they're looking for a needle in a haystack, that's the proverbial needle in a haystack: the classic, instantly recognizable example of something nearly impossible to find.
The word often appears as “the proverbial,” as in “the proverbial elephant in the room” (an obvious problem everyone ignores) or “the proverbial last straw” (the final small thing that causes a big reaction). Using “proverbial” this way signals that you're using a well-worn phrase on purpose, because it captures the situation perfectly.
Sometimes people use proverbial more loosely to mean “famous for” or “known for,” as in “his proverbial kindness” (he's famous for being kind) or “her proverbial sweet tooth” (everyone knows she loves sweets). In this sense, it means something has become so characteristic of a person or situation that it's almost legendary.