12v is the voltage, this is what matters most--too much will fry your board, too little won't work.
30A is the amp RATING: it's the maximum amps that the power-supply can provide without burning out.
360W is redundant information. Watts are just amps * volts. It's a shorthand to quickly describe how powerful a supply is, but you can just do the math yourself: 12x30 = 360.

The best way I've found to explain volts, amps and watts is to think of electricity like water flowing through a hose.

volts = how fast the water is moving through the hose
amps = How thick the hose is
watts = how much water is coming out the end of the hose (a function of how fast the water is flowing and how thick the hose is).

If the water isn't moving fast enough (volts) there won't be enough force to make your machine work.
If the hose isn't big enough it will burst if the machine trys to draw more water than can fit in the hose.