The word "muster" means the act of assembling, which is what passengers and crew do during the mandatory safety briefing on every cruise that's referred to as a muster drill.
Per the International Convention for the Safety of Life at Sea, all passenger ships must have a cruise muster drill during the first 24 hours of the trip. The drill mimics a nautical emergency, allowing passengers to familiarize themselves with the sound of the alarm and to learn all of the information they'll need to know in order to stay safe in the event of an emergency at sea.
Every ship has designated muster stations, which are meeting points for passengers during an emergency, typically on the open decks by the lifeboats. They are usually organized by proximity to cabin location, and the crew keeps a record of all names assigned to that muster station so they can take a roll call and make sure everyone is accounted for. Cruise ship muster drills usually call for passengers to meet at their muster stations (designated on the safety sign in your stateroom), though on mega-ships, passengers might assemble in a larger space, such as the theater, that can accommodate more people for instruction.
During the muster drill, the emergency siren is sounded, so passengers can familiarize themselves with the sound. The ship captain and crew will go over safety procedures, including pointing out where life jackets are and demonstrating how to don them quickly. (Passengers often need to bring their life jackets to the muster drill and put them on once there.) Crew members will also explain the best escape routes in case people need to leave the ship in an emergency situation.
Everyone -- even children -- must attend the muster drill, even if you've sailed on the same ship or cruise line previously. Passengers should also stay quiet and follow instructions during the drill, so everyone can hear the safety briefing.