In Act I, these members of the royal family of Naples and some of their courtiers and their servants and such are on a ship on their way home. They've been at a wedding in Africa where one of the king's daughters was getting married.
On the way back, their ship is hit by a terrible storm. Because they are used to being in charge, the royal people keep interfering with the sailors. They come up and try to tell the sailors what to do and they keep wanting to talk to the captain. For example:
Good Boatswain, have care. Where's the Master?
[To the Mariners] Play the men!
The boatswain keeps trying to get them to shut up and go back to their cabins because they are in the way. When he does that, they curse him and generally are jerks toward him.
Hang, cur, hang, you whoreson, insolent noise-
maker! We are less(40)
afraid to be drowned than thou art.