A ship's company is, of course, her people without whom she is nothing more than a shell of wood with a web of rope around her. Spirit she will always have, but she only comes to life because of the men and women who love her enough to keep her clean and weatherly. Her company.
But there's more to it than that and many of the word's meanings are nautical. According to my old friend Webster, the word company came to English via the Old French word compainie. There are twelve meanings listed in my printing and most of them relate nicely to the nautical usages. Excepting, of course, Company of Jesus: Jesuit which see (and we all know men of the cloth are right bad luck aboard us, mate).
The idea of a ship's crew being her company translates to land as a company of soldiers or other military men; a group united under one commander. This idea grew larger with the formation of the various East India Companies in the 17th century. The word was morphed, through this mercantile association, into it's common modern usage for business. Initially company in this sense meant the people who belonged to or worked for a firm but whose names were not incorporated into the firm's name. Eventually "company" or "Co." simply came to mean the firm itself.
Companion is another common word aboard ship that stems no doubt from company. A companion is an opening in a ship's deck leading to a private cabin. A companion ladder is either that which leads to the cabin in question, or the ladder by which the quarterdeck is accessed from the waist of the ship. Occasionally the ship's dog, who may spend his or her whole life aboard like our old friend Hatch, might be known as the ship's companion. A man who is companionable is more likely to get along well in the little wooden world that is a ship.
So there you have it, Brethren. May the wind fill your sails, the sea follow, and may you always be in good company.