The spool is where all the line for the fishing rod is stored. It does not perform any specific function, but all other parts of the reel relate to this central piece. Fishing line is wound around the spool, and, as it unwinds, it spins the spool. How the line is released from this spool is controlled by various triggers and brakes attached to the spool.
The thumb bar is a more advanced form of the trigger release found in simple fishing rods designed for beginners. This button controls how freely line is able to be pulled off the reel--for a slow release, the thumb bar is only pressed slightly. This bar is pressed in fully when casting deep--when pressed in all the way, the thumb bar relieves the spool and fishing line of all tension and friction, allowing it to flow freely.
The drag set is key to setting the hook in a fish's mouth. It is a small wheel located on the side of the spool that controls how quickly line is pulled from the spool. The drag set is usually kept loose, until the line is cast, at which time, the wheel is turned to the proper setting. Anglers seek a very delicate middle ground--they require enough tension for when they need to forcibly pull the line, so that the hook punctures the fish's mouth, but the tension cannot be so tight that the abrupt pressure snaps the line. The drag set's key function is allowing for this flexibility--without it, you would hardly ever be able to set the hook properly.
The reel brake works in conjunction with the thumb bar to control spool speed. Its most valuable characteristic comes into play when you are casting down to the bottom of the lake. Your brake settings stop the reel from spinning when your lure or sinker touches bottom. Without it, the kinetic force of the spool would keep it spinning, letting out too much line, and making it difficult to tell when a fish came by for a nibble.