The A in the 1A, 2A etc means the current (AMPS) it can provide. There are a few things with power, namely V (volts), A (Amps), and W (watts, also sometimes expressed as P (power)). The formula which relates this is P (or W)= V*A. Watts = Volts x Amps. That's how much current can be provided and how much work can be done at that particular voltage.
Volts is electrical potential. Amperage is current flow. You can have 10,000 volts at .0002 amps and it won't hurt you one bit. It'll tickle you and could also put on a pretty electrical show. But 120v @ 1A could kill you.
So - 5v @ 1A = 5 watts. 5v @ 2A = 10 watts. This allows you to calculate what kind of PSU you will need based on power draw.
IE: you have a RX-480...