A galley is a long ship propelled by oars, and possibly sails as well. You're not likely to see a galley these days: they were used from ancient to medieval times.
You may have seen movies portraying old ships with dozens of rowers, lined up on benches. Those ships are galleys. Galleys were used for more than a thousand years, and they played an important role in both war and trade. If someone today says they’ve been in a galley, you can assume they aren’t referring to this kind of ship. They probably mean the galley, or the kitchen area, of a ship or airplane.