Yes, basically double means that the alcohol level is greater than an "ordinary" beer which would be qualified of "simple" (but that term never appears). Double is around 7%, triple around 8/9% and there are also quadruple.
One other meaning is about the number of fermentation steps, but historically that's not the true meaning and more of a recent marketing argument, because all "special beer" as we say in Belgium have 2 fermentations. The main one transforming sugar to alcohol and a secondary during the "keeping" period, usually in bottles and helping to develop the specific taste of the beer. Some recipe includes adding some yeast to refine the taste, so some brand speak about triple fermentation.
Sorry if the English terms are not the best, I tried to explain from what I know but I don't know beer specific wording in English so I translated literally from French for the words I didn't knew.