Updated October 2, 2017
The bridge is the place on the ship where the captain and his crew manage the direction and speed of the ship, as well as other functions of the vessel. The nautical term originated from the narrow, raised platform "bridging" the two sides of a large vessel that allowed a captain access to both sides while commanding the crew.
Modern cruise ships normally have a glass-enclosed bridge on an upper deck near the front of the ship giving the captain and crew a clear view forward. Enclosed or open-air wing-like extensions perch out over both sides, extending the crew's ability to see toward the rear of the ship and even downward to the water through windows in the floor of those "wings."
On the bridge, the crew will have paper nautical charts as well as computer equipment that controls and reports on the ship's mechanical, electronic and communication systems; its global position; and its route to the next destination. Steering capability is duplicated in several places, both mechanically and electronically, including in the wing extensions where the captain controls the vessel during docking, often with the aid of a pilot brought onboard from the port.
Most cruise ship bridges are off limits to passengers, though some lines do offer bridge tours or visits as part of behind-the-scenes ship tours. Some cruise lines with smaller ships (such as Windstar and Star Clippers) have an open bridge policy, allowing passengers to stop by the bridge and chat with the officers whenever they like -- except during more intense maneuvering such as docking and during bad weather.