Generally, what the device can tolerate being run through it. So the latter, what it can dissipate. In many cases the two numbers will be close to the same, but you'll generally want to ensure you've got at least a few watts in reserve rather than redlining the parts.
The 'Power - Max' field is generally held to be what power you can safely run through the device, as rated by voltage times current. Putting ten watts through a hundred milliwatt rated trransistor will burn up the transistor, as the wattage calculation accounts for power not being dissipated by the device. The field is meant to be intuitive.