A briefcase was a type of rectangular carrying case used to transport important documents.
In 2004, Loomis picked up his payment in a briefcase. (ENT: "Carpenter Street")
In 2365, The Comic's hologram told Data that he found a briefcase that looked like a fish hysterical. (TNG: "The Outrageous Okona")
In 2372, Odo took the form of a briefcase in order to gain admission into the Federation president's office. (DS9: "Paradise Lost")