What does Current mean in a power amp???

Ohms law is not really a good way to figure current output of an amplifier. Ohm's law works in a purely resistive DC circuit. The output of an amplifier is AC. You generally will be required to factor in inductance, capacitive reactance and pure resistance (this makes up impedence)to come up with the current output into any given load. Amps that "Double down" are always better for driving low impedence loads. However, things can happen to an amps output when the load has steep phase angles and high reactance. Look at the dbw that Stereophile uses in rating amps for some reference. The bottom line here is that each amp will behave differently into the reactive load of different speakers. A resistor on the test bench doesn't mean a lot.
With this said, current is the ability of the amp to deliver actual power expressed in watts into a given load. Power(in watts)= volts x amperage This is a simplification of a more complex calculation.

There's one other factor with an amplifier that envolves its feedback circuit. This also affects how the amplifier "sees" its attached load. Some manufactures install small coils of wire (almost like a choke) on the output to prevent the amp from ringing into loads it doesn't like.
As Sean said, this is much to complicated an issue to be summed up in a simplistic Ohms Law formula that was designed for DC circuits. You can't even apply it to the resistance in a piece of straight wire. Once you apply AC to it, the wire can react rather strange(depending on its composition)
They use to use actual current limiting circuits to keep the amp from overheating.
My best advice is to decide what type of speakers you are going to use an experiment around until you find a good amp to match. Way too many variables to say an amp is right based on specs. Amps that "Really" double down are a good place to start. Some of the best sounding amps---well you're not going to worry about current(eg. the Pass Labs Aleph 3)One heck of a good sounding amp at 30/ch into 8 ohms and about 45 into 4. It drove a lot of speakers well as long as you didn't want to rock a hall!