When ${\mathrm{KClO}}_3$ is heated, it decomposes into $\mathrm{KCl}+{\mathrm{O}}_2$. If some ${\mathrm{MnO}}_2$ is added, the reaction goes much faster because

${\mathrm{MnO}}_2$ acts as a catalyst

${\mathrm{MnO}}_2$ provides heat by reacting

${\mathrm{MnO}}_2$, decomposes to give ${\mathrm{O}}_2$

Better contact is provided by ${\mathrm{MnO}}_2$