This is just a fancy term for words that mean more than meets the eye. Figurative language uses figures of speech like similes and metaphors to build meaning beyond the literal. Think of figurative language as words that have more than one level of meaning.
We often use figurative language in our everyday speech without even realizing it. When we say "it's raining cats and dogs," we don't literally mean that felines and canines are falling from the sky. It's a metaphor for a major downpour. Here are a few other examples:
Get the picture? Hey, that's one, too.
Check out figurative language in John Keats's poem "When I have fears that I may cease to be," Ernest Hemingway's short story "Hills Like White Elephants,", and Bob Dylan's "All Along the Watchtower."