Watts are basically the power you put through your atomizer or cartomizer... When you vape @ 3.7 volts, and use a low resistance 1.5 ohm atomizer, the vape is good. Now if you took that some voltage, and used a 3 ohm atomizer instead, you'll get diminished taste and vapor. Reason being is that the watts, or total power getting to the coils is less due to a higher resistance... Now take that 3 ohm atomizer and turn it up to 5 volts and you've got a similar quality vape, because the wattage is about the same.
There are devices out there such as the kick or the darwin, that you actually set the wattage on, and it adjusts the voltage for you so that the same power is going through your coils no matter what is attached. We may see more of these types of devices in the future, but for now that's it. Most people tend to like between 8-10 watts for their sweet spot... (which is typically just under where the juice starts to taste burnt) To figure out the wattage, take your voltage squared and divide it by the resistance of your atomizer.
Hopefully that makes sense, if you're still having an issue understanding, the best analogy I can think of is a car one, voltage is to horsepower as watts is to torque... People buy based off the voltage number (or horsepower), but in reality what you feel is the watts (or torque). There are tons of ohms law calculators on the internet (do a quick google search) and you can play around with different voltage and resistance combinations to see how many watts you are at and also when you will hit your amperage limit of the device (lavatube v1 and v2=2.5A, lavatube v1.5=3.2A, ProVari=3.5A, Lavatube v3=4A). Hopefully that helps...
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