A figure of thought is a rhetorical device in language. Very broadly, it is a method of presenting ideas, feelings or concepts in an artful way. The method of presentation is different than what a person might consider "ordinary." Also known as a topic of invention, a figure of thought usually makes some connections to a person's sense of logic or emotions. It implies more than what is actually is said, forcing the listener or reader to draw on his own experience and culture for meaning.
If someone says, "Words cannot express how upset I am," they are using a technique known as aporia. This technique says there is no way to talk about it, but with this phrasing, they still get the concept of being upset across, call on the listener or reader to understand that the degree of distress is high, and get the reader or listener to think back on his own upsetting experiences for reference. This is much different than using very literal terms to explain what is wrong, because the person is communicating via concept.
Sometimes people confuse figure of thought with figure of speech. These two devices are closely related in purpose but are not identical. The primary difference is that a figure of speech often uses specific words and word orders that become commonplace or even cliché due to use; it essentially works like another word in the language. An example is saying a girl is "pretty as a picture." With a figure of thought, the exact word choice and order is less important than the overall, larger idea behind the communication.
Due to the similar purpose of and confusion between a figure of thought and figure of speech, even professional linguists do not always agree on how to classify specific figurative devices. This is evident in examining lists of the devices. In reality, there sometimes is some overlap. Some linguists argue that the distinction between a figure of thought and figure of speech is not particularly necessary.
The purpose of a figure of thought is twofold. First, it improves the larger aesthetic impression of the communication, making it seem more elite, mastered or beautiful. Secondly, a figure of thought allows an individual to get across more abstract concepts that truly might not be definable with concrete terms. In some cases, using a figure of thought ends up being more concise than if a person tried to describe everything behind the idea.