Tom Swifties are an unusual form of wordplay. They take the form of a character (usually, but not always, named Tom) saying something. The wordplay comes in the way in which it is said. In a typical example, the adjective used to describe what Tom says plays on what was said, but they can also get much more complex than this.
For example: "I plan to work in a cemetery," Tom plotted gravely.
The name 'Tom Swifties' comes originally from a series of stories by Edward L. Stratemeyer, which featured a character named Tom Swift, who's speech was scattered liberally with adjectives describing how he was saying things. In this form it was not a wordplay, but in fact simply the author's laboured avoidance of the simple word "said".
Later, another writer took up the idea and satirised it, and in a clever parody of the original stories turned it into a unique form of wordplay.
The best way to find out about Tom Swifties is to see some examples. BadPuns.com has a section dedicated to them, so there are plenty of examples to see.