The watt rating of a LED flashlight is supposed to mean how much power it uses, and in most cases is the peak power limit of the LED as it takes electric energy and turns it into light, and heat. In general, higher wattage LEDs output more light than lower wattage LEDs.
However, many LEDs are under-driven to take advantage of the LED's voltage vs. current operating curve, and voltage vs light output curve. Some lights use a LED capable of consuming 3W, and will run it at 1W because it will be more efficient than a 1W LED at maximum power.
And yes, a light that consumes more power will indeed drain batteries more quickly than one that uses less power.
Exactly what this means in practical use is a bit different. Many manufacturers will claim the maximum power of the LED in a light, others will claim what the LED is being driven at. Power generally corresponds to brightness, but there are many different LED designs, so you can see varying levels of efficiency among LEDs of the same light output.