How does sulfuric acid catalyze the reaction of potassium chlorate and sucrose? Part of the total reaction is mentioned here:

http://chemistry.about.com/od/demonstrationsexperiments/ht/instantfire.htm

$\ce{2KClO3(s)} + \text{heat} \rightarrow 2\ce{KCl(s)} + 3\ce{O2(g)}$

The rest is a mystery. (And where does the heat come from?)

I regret to say that I have delayed acquisition of organic chemistry principles that might have answered this question already but can't help but wonder why, right now.

I feel that once the role of sulfuric acid is cleared up, the reaction with sucrose not described above will explain itself.

(And no I am going to run around burning things down with this knowledge.)
I think the sulfuric acid isn't really a catalyst here -- I think you use the heat from the reaction between sulfuric acid and sucrose (which will start happily at room temperature) to start the reaction between the potassium chlorate and the sucrose (which usually won't).

ETA: Once you've done that, it's pretty much a straight-up messy combustion reaction, only with the oxygen being provided from a solid source (thermal decomposition of chlorate to chloride and oxygen as the reaction you mentioned shows) rather than anything mechanistically clean. Compare, for example, this fairly typical demonstration just using hot chlorate and a sugar source: Oxidation of Sugar or Gummi Bear with Potassium Chlorate.