Lamp power of incandescent lamps used to be measured in "W" - the electrical power rating. But this measure is totally unsuitable for LEDs, as it describes the power consumption, not the light output. With filament lamps, efficiency was constant over the last decades, but LEDs are evolving. Better (usually more expensive ones) get available, but also cheap poorly performing ones. Measuring LED performance in W is like rating a car by its l/100 km consumption - is a 12 l/100km car better than a 7 l/100 km one? It depends - on engine power in this case.
For illumination (LEDs in particular), the light output in lumen is the one that is most relevant. It tells you how much light you get in total from a lamp, independent of the beam angle. Focusing the beam achieves a higher peak intensity, but the luminous flux measured in lumen stays the same. To get a feeling what a lumen is, you can take incandescent lamps as comparison - normal bulbs have 12 lm/W (halogen: 20 lm/W), so a 60W bulb has 720 lm, a 20W halogen bulb 400 lm.
Finally, the power rating of a lamp in W is important - but the lower, the better! For example, let's compare two lamps having both 500 lm output, lamp A with 5W input, lamp B with 10W input. Is the 10W lamp better? No, on a 20 Wh battery the 10W lamp would run for two hours, while the 5W lamp would last four hours - with the same amount of light! For that reason, we have detailed run time tables which show you how long our lamps burn on each setting. Our run times mean constant light output - not some fantasy number starting with bright light and at the end dropping to full moon intensity!
A last thing. If you consider buying LED lamps for household (interior) lighting: Most of them, particularly the MR16 halogen replacement types, perform very poorly. Fantastic numbers like "60 LEDs" try to suggest you get a lot of light. What you probably do is save energy. An LED bulb with 1 or 3 W does consume less than a 50W halogen of course. But the primary function of a lamp is to provide light! These replacement lamps (often seen for hefty prices in DIY stores) mostly have miserable efficiencies like 50 lm/W. This means you might swap your 50W halogen (1000 lm) to a 2W LED (100 lm?), giving you 1/10th of the original brightness, often with a bluish tint (result of poor quality overdriven LEDs). To avoid such disappointments, only buy LED lamps if they have a lumen rating. Compare it to what you have currently installed. For living room use (not cellar lighting), check the light color (color temperature in K). If no ratings are given, assume the worst (and stay clear).