To expand on what rover said:
a commision is, or possibly was, a physical, signed document, given to the officer by the head of state (or someone acting in his name), and in past times signed by the head of state personally (the king/queen of england used to sign british commisions right up until 1900, when the losses in the boer war made this impractical).
the dosument was the officers proof of his status as an actual officer, in the same way a passport is proof of your nationality. it sperated the bearer form the non-commissioned officers, like the sargents and warrant officers,
Can you work on a ship without being commissioned? Can you be commissioned without ever being promoted?
as an crewman? yhea, of coruse, as an officer? strictly speaking, no, but you can be promoted on the spot, a "battlefield commission", which are normally confirmed by the hierarchy (assuming you don't screw up).
In any case, in modern useage, being Commissioned means being an officer, rather than a NCO or enlisted soldier. when you become an officer, you get given the commission without doing anything extra beyond whatever you did to get promoted. the commison is just a bit of paper that says "this mn, <name> is an officer of the <service>, who was promoted on <date>".
that last part is quite important for the officer, as the date on his commison is the basis of his senoirity, which determines the chian of command within rank (ie, who commands who when both have the same rank. oldest date wins, with expections).
also, you can be commissioned directly into any rank, not just 2nd Lt. In the british army, at least, a lot of senior Warrant Officers, men with 15-20 years of service and a vast amount of knowledge of combat, are sent though sandhurst and are commissioned as captains.
as Rover said, a "captain" in the naval service is much more senior than a army "captain" (a naval captian is the equivilent of a full Colonel in the army (OF-5). A army captain is the same rank as a navy full Lieutenant (OF 2)