The Conn
This refers to who has physical control of a vessel at any particular time. To “have the conn” means you are in final control of the navigation of a seagoing (or spacefaring) vessel.
The captain of a ship assigns the conn. They can give it to a junior officer and take it back at their discretion. Command of a ship is always with the captain – possession of the conn just indicates who is responsible navigating the vessel at any particular moment, and provides a clear, verbal demarcation of control (“You have the conn.”).
There are disagreements as to whether it’s short for “control” or “conduct” (or even a Celtic word for “head”), but over the years, it’s become a noun in and of itself.
Why I Looked It Up
I had heard the term in Star Trek episodes, and knew the basic idea, but I always thought it should be “the com” meaning command. (As evidenced by this this Stack Exchange question, I was not the only person who got this confused.)
Then, in the ship-faring scenes Shogun, the term was also used several times (though, with just one “n”).