Proverbial is an adjective that can either mean that it has to do with a proverb, or that something is common knowledge or known about by many people. It is mostly used to modify a word or phrase within a well-known proverb or idiom. The adverb form is proverbially.
A proverb is a common saying that imparts truth or advice. It is usually short and concise. In the Bible there is a whole book of these sayings aptly named Proverbs
However, sometimes people use proverbial when they really mean figurative.
Figurative is an adjective that is synonymous with metaphorical, it means to be representative of something else or another meaning beyond the basic understanding. The figurative meaning of an idiom is the implied meaning, or in other words, not the literal definition of the words.
A general rule: use proverbial when it relates to a proverb and figurative when it relates to a figure of speech. Of course, the case may be made for something being both a figure of speech and a proverb, then use your judgement.
There were three reactions when we read the report that sources are saying the Celtics plan to “swing for the proverbial fences” this summer. [Boston Herald]
[R]egulators are like “the proverbial ostrich–head firmly entrenched in the sand” when it comes to understanding how these rules divert capital from creating real economic growth. [The Wall Street Journal]
Churchill often gets credit for coining that metallic metaphor—on that stage—for the figurative barrier drawn across Europe between the capitalist West and the communist East. [TIME]
That much was clear Wednesday morning during a tense, 80-minute oral argument inside a packed Supreme Court chamber, where top members of the Obama administration and Congress watched anxiously for the figurative white or black smoke. [USA Today]
My co-finalists in the continental Babishai Niwe Poetry Award and our Femrite hosts were gushing, fanning a figurative flame in my face. [The Star]