Non technical answer, wattage is a measure of the usage of electricity the bulb uses, how much energy it takes to run the bulb. Household bulbs are measured in Watts for some reason and its what most people are used to, but also why you will see bulbs listed as 15W bulbs with the output of a 60W bulb, etc.
Lumins are a measurement of light intensity. Ideally the way to measure would be lumins of light at the subject, so if your putting something in the bottom of the tank and had a submersible meeter you could find exactly how much light was hitting that peice of coral. (Sort of like using a light meeter in photography.)
-Scott