A swagger stick was a short stick, similar to a cane or baton, often carried by high ranking military officers.
In 2285, Captain Lawrence H. Styles was known for commanding his ship, the USS Excelsior, while carrying a swagger stick. (Star Trek III: The Search for Spock)
James B. Sikking's portrayal of Styles emulates another character Sikking played in the television series Hill Street Blues, who also often carried a swagger stick – in this case, as a homage to George Patton.