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It means that the resistor will safely dissipate the heat involved in transporting that much power through, without burning up/out. If you exceed that rating, the resistor will become too hot for its own good.

Power is always linked with Voltage and Current, and Current is linked with Voltage and Resistance of the resistor. You will do well to remember the tandem of laws:

Power [Watts] = Potential [Volts] * Current [Amperes]

and

Current [Amperes] = Potential [Volts] / Resistance [Ohms]

For example, if you have a 100ohm resistor rated at 0.25W, then to satisfy that requirement, a voltage of no more than 5V can be applied to it, because 5V / 100ohm = 0.05A, and 0.05A * 5V = 0.25W.

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Q: What does one-quarter W mean for a rated resistor?
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