Speakers generally have an average or nominal wattage (power) rating and a peak wattage (power) rating.
Power is energy per time. It is measured in watts. Power delivered by an amplifier to a load (speaker) is normally determined by dividing the voltage (V) squared by the impedance (Z) :
Power = V² / Z
The resulting type of power will depend on what voltage we use. If peak voltages are used, then the result is peak power. If RMS voltages are used, then average power is obtained. RMS (root-mean-square), is only a mathematical method to extract the mean value of an alternating signal (one with negative as well as positive values).
Average or nominal wattage: Often wrongly referred to as "RMS" power, since it is derived from RMS voltage readings. RMS (root-mean-square) only makes sense on variables that have negative as well as positive values. Power is only positive (goes from the amplifier to the speaker, not the other way round), so does not need the "root" and the "square" of the RMS process (which just extract the sign out of a number), just the "mean" (average). Average power is therefore that which uses RMS voltage for its calculation.
Peak power. Corresponds to the calculation of power based upon peak voltages.
What all that means in the real world is that a speaker RMS wattage is what you want to use when you match it with an amp.
Example: You have a decent bookshelf stereo that is rated at 100 watts per channel PEAK power at 8 ohm impedance. Surfing ebay you find a great deal on speakers that have a 50 watt, 8 ohm impedance, RMS rating. Since it's an RMS rating, as a general rule of thumb, their peak power rating would be twice the RMS rating. In this case 100 watt peak power, the same as your bookshelf system, so your stereo wouldn't blow these speakers out.
Conversely if your stereo is rated for 100 watts RMS at 8 ohms and the speakers you find are rated at 100 watts peak, then the RMS rating for the speakers is probably only 50 watts and your stereo will blow them out.
Keep in mind through all this that more power doesn't always = louder or better sounding.