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.)