Table talk is a literary genre, a species of memoir. A collector (biographer, colleague, friend, etc.) records impromptu comments by some famous person (made generally at the dining table or in small get-togethers), in anticipation of their lasting value. The precedent in classical literature was the symposium, such as the Table Talk of Plutarch, though this was a supposed memoir of an occasion, rather than a person.
"Table talk" may also refer to a similar informal conversation, more deliberately engaged in by the famous person, with the direct intent of publication (somewhat analogous to granting an interview).
Collections of such table talks by royal persons, celebrities, and other important personalities dating back to the 3rd century exist. The phrase table talk has been in use in the English language since the 16th century.
As examples, published table talks exist for:
Occasionally, comments are collected from others by a notable person as part of that person's working notes and may survive in the papers of that person. Ralph Waldo Emerson, for example, kept notes on the conversations of his family and friends, many of whom, of course, were noteworthy.