Definition of a "Tom Swifty" from "The Random House Dictionary of the English Language", 1st edition (1966):

Tom Swiftie, a play on words that follows an unvarying pattern and relies for its humor on a punning relationship between the way an adverb describes a speaker and at the same time refers significantly to the import of the speaker's statement, as in "I know who turned off the lights," Tom hinted darkly. [named after a narrative mannerism characteristic of the Tom Swift American series of adventure novels for boys]

In actual use, "Tom Swifty" seems to have a somewhat broader meaning, and includes the form christened "croakers" by Roy Bongartz, wherein a verb rather than an adverb supplies the pun (e.g. "I'm dying", he croaked). "Who is this Tom Swifty character anyway?" asked Tom unselfconsciously.

Tom Swift was the brainchild of Edward L. Stratemeyer (1862-1930). Stratemeyer first used the name "Tom Swift" for the title character in "Shorthand Tom; or, the exploits of a young reporter", serialized in 1894. Sixteen years later he reused the name for a new character, an ingenious youth whose amazing scientific inventions and discoveries would carry him to weird and wonderful places. The Tom Swift adventure series, which was published under the pseudonym Victor Appleton, began with Tom Swift and his motor-cycle; or Fun and Adventure on the road in 1910, and continued until 1935 (5 years after Stratemeyer's death!). Stratemeyer was also the creator of the Bobbsey Twins, Nancy Drew, the Hardy Boys, and other lesser-known series. Stratemeyer only supplied the characters and the (repetitive) plots for his books; he had a syndicate of some 20 hack writers to do the actual writing. The chief actual writer of the Tom Swift books was Howard Roger Garis (1873-1962). After Stratemeyer's death, the syndicate was taken over by his daughter, Harriet S. Adams, who in 1954 started the "Tom Swift, Jr." series under the pseudonym Victor Appleton II.