Definitions for "Power Handling"
The highest Safe Power for Speakers. But it is far easier to Damage Speakers with an Amplifier of too little Power driven beyond its Capabilities, than with an Amplifier with too much Power used with Discretion.
A power source (receiver or amp) is required to drive any car speaker. The low number listed is the absolute bare minimum wattage required to get acceptable sound from the speaker, and the high number is maximum amount that the speaker can handle for an extended time. For best results, match your power source level (RMS, or continuous watts) to the upper part of the speaker's recommended range (RMS).
The safe power level that a speaker can handle without destroying the drivers. It sounds crazy, but you run more risk of damaging speakers using an amplifier with a power rating (watts) lower than the speaker units. For example, a 100 watt amplifier driving 50 watt speakers is not working very hard so the speakers receive a fairly low-powered, clean signal. A 40 watt amplifier driving the same 50 watt speakers will be working close to its limit to provide a signal strong enough for the speakers. This reduces the quality of the signal, creating distorted electrical currents that speakers don't like. Think of it like a Ferarri racing car and a basic Ford Fiesta. Both will easily cruise at 80 miles-per-hour, but the Fiesta will be working extremely hard, while the ferarri will far from its limits. The Ferarri will last longer because it is working less, while the Fiesta is more likely to fail due to stress.