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dynamic power is the absolute max an amp can put out for a short period of time..
this is the pwoer output during short "beats" like bass drum hits or cymbal crashes, etc.

RMS stands for "root mean square".. it's bssically the "long term output" of the amp.. it can constantly deliver this power, as long as you keep the sucker cool and feed it enough power.

correction
 

What dude said about rms is correct. But dynamic power is not the same as max power. The term dynamic power is used by some amp companies that rate their amps conservatively for competition use. Mtx for example does this. Dynamic power is power at (i think) 14.4 volts, which is average output for an alternator when the car is at idle. The lower power rating is for at 12 volts when the car is not running. This conservative rating is so you can enter lower classes at comps. The power output jumps the same way your lights get brighter when you start the car. Max power is mostly unimportant. Rms is very important. Dynamic power is important when you are comparing something like an mtx or alpine v12amp, both measured at 12v, to something like a pioneer, kenwood, rockford, sony, ect amp. It it is only a valid comparison using the same voltage, which most amps are rated at 14.4. Crutchfield catalog has a good comparison chart. By the way dynamic is rms power, its just the difference in source power voltage. hope this helps.

Just to add to what mrloyd said:

I have two MTX amps. One is rated at 50x2 @ 12V, but all MTX amps come shipped with true performance numbers. My amp puts out 89x2 @12V and 201x2 @14.4V all at 4 ohms. So you can see that MTX greatly underrates their amps. My other amp has similar specs except that it's a four channel.