Resistor wattage ratings are:

A resistor's primary function is to oppose current flow, and in doing so, it converts electrical energy into heat. If a resistor cannot safely shed this heat into the surrounding environment, it will overheat and eventually fail. The wattage rating of a resistor specifies the maximum amount of continuous power it can safely dissipate as heat without sustaining damage. This is why high-wattage resistors are typically physically larger; they require more surface area to radiate heat effectively. While physical size gives a hint about a resistor's ability to cool itself, the rating itself is strictly a measure of its heat dissipation qualities. Distractors mentioning joules are incorrect because joules measure total energy over time, whereas watts measure the continuous rate of power (heat) dissipation.