Using a secondary container to let the beer clear up and so that it's not sitting on the trub (yeast and such at the bottom of the primary fermenter) and for aging purposes. In this context, no additional sugar is added. It doesn't really ferment more in the secondary though it may finish fermenting depending on when you transfer the beer to it. That it is called "secondary fermentation" can be a little misleading.
Once the beer is finished fermenting, using time and a hydrometer as your guide, you do bottle with priming sugar. This is a sort of controlled, mini-fermentation whose intent is to carbonate the beer in the bottle.
Secondary fermentation is unnecessary in almost all instances.
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