clutches are usually sold with the pressure plate. the flywheel bolts to the crank, the pressure plate bolts to the flywheel, and the clutch disc is sandwhiched in between. the clutch disc is connected to the splined transmission input shaft. when you step on the clutch pedal, you are pressing a throwout bearing against the springs of the pressure plate, releasing the clutch disc from the flywheel, and thus disconnecting the transmission from the engine.
the higher stage clutch means the more torque it can hold by way of stiffer diaphragm springs or a "better" friction surface. stage 2 is fine for N/A racing shifting at high rpms. I wouldn't go to stage 3 or higher unless I had F/I.
but really..."stage" is just a marketing term to make clutch selection easier and relative within brands. the stages don't necessarily carry over from brand to brand. you either know the construction of the clutch, or just know the exact product perhaps by word of mouth or a forum suggestion.
a higher stage clutch will engage faster. meaning there is little gray area between being fully engaged and fully disengaged. race clutches (stage 4 or 5)are definitely either on/off. this is obviously not very streetable.
higher stage clutches on the whole will have a relatively shorter life if used on the street. the material that grabs and holds better will not last as long. however their ability to hold more torque when racing means they will wear less from racing, because a slipping clutch on the street or track wears fastest.
on some stage 1 or 2 clutches you may notice a slightly increased pedal pressure necessary to disengage the clutch (maybe 15%).