Every ship/sub has a rotating team of officers and enlisted sailors who "control" the movements of the ship during regular shifts that rotate around the clock, 24 hours a day, called "Bridge Watches". There is a rigorous training schedule to qualify officers to be the "Underway Officer of the Deck" that involves everything from written tests to hundreds of hours spent on the bridge in on-the-job-training. The designation is given by the Commanding Officer (CO) himself, who is probably an O-5 or Commander. It means he has utmost confidence in the ability of the designated officer such that the CO can go to bed at night and sleep knowing that the officer can control and command the ships movements as well as the CO himself can and can handle any emergency that can come up. It is a tremendous responsibility that is not given easily by the CO and is prized by the junior officer. That is what that video film clip is referring to. I can also assure you the CO sleeps not 10 feet from the bridge and his standing orders to the young officer is "wake me immediately if anything changes" from the night sailing orders. During the day, the same thing occurs with the CO prowling around the ship and off the bridge doing everything he needs to with the control still being done by another young officer on the bridge with another Bridge Watch team.The CO seldom takes control of the ship on the bridge unless it is a really touchy maneuver that he wants to do (coming into port and alongside a pier is the classic example) or he wants to demonstrate to an officer in training how to do something. The best COs are constantly teaching and coaching his/her officers on ship handling and the worst won't let them do anything.
The most junior true Commanding Officers I have ever heard of were O-2s on Swift Boats, O-3s on the various WHECs and metal gunboats that cruised rivers and coasts, and the old minesweepers during the Vietnam war, none of which exist anymore.
Since you are looking for information about a Navy junior officer duties (same with CG too) let me elaborate a bit on what that young officer does on a daily basis. Every Navy officer has at least two major jobs---one is your "day job" as a division officer in charge of about 15-30 enlisted sailors and has the title like Gunnery Officer, Torpedo Officer, Damage Control Officer, Communications Officer and so on. You have a senior enlisted person such as a Chief or First Class to help you run the division. The second job you have is on one of the rotating Bridge Watches noted above. Your day is interesting as you may be on the Bridge Watch from midnight to 4am, you get to hit the rack for 2 hours but then are standing in front of your division to begin a normal workday. You may go back on the Bridge Watch from noon to 4pm, get off to finish up what you couldn't do while you were gone that afternoon , eat and hit the rack as you will be woken at 3:30am to be back on the Bridge at 4am. You get off the Bridge at 6am but no rack this time as your work day starts again at 7-7:30am and you want to eat too. There is no excused time to take a little nappy-poo during the day as everybody is on the same rotations. As a junior officer you always get lots of extra duties like Classified Material Custodian, Ship's Historian, Mess Officer just to fill any extra minutes you may have laying around. Now mix all this in with gunnery exercises, chasing subs (or vice versa), coming alongside carriers and oilers, maneuvering in large formations, fire drills, flooding drills, and losing electrical power such that everything is pitch dark, and the days really fly by. You will be plenty busy learning the ropes for many exciting years before Uncle Sam trusts you with a ship and one of the biggest things will be how well you lead, train, take care of, and the performance of your enlisted troops. Welcome Aboard Ensign.