Your equation is NOT balanced, unless you have entered it wrongly of course. So let's start by balancing it.

KClO3(s) --> KCl(s) + O2(g)

First find an element on each side of the equation that is in only one compound on each side and is not balanced.

Although we usually leave oxygen to be one of the last elements we balance, in this case it is the only one not balanced at present, so we start there - multiply the O2 by one and a half to balance the Oxygen

KClO3(s) --> KCl(s) + 1 1/2O2(g)

There are now the same number of elements of each type on each side - it is therefore balanced. But we don't like halves in equations, so multiple everything on both sides by two:

2KClO3(s) --> 2KCl(s) + 3O2(g)

We now have a perfect result. This equation is an example of a decomposition reaction.

The KClO3 decomposes into two other compounds.