Every problem can be broken down into a collection of factors which affect each other in various ways.   Some might have relationships that can be described using physical laws, some (like noise) can be measured experimentally, some might only exist statistically, and only some of the time, and some factors might seem to be correlated, but are actually independently determined by a third, unknown variable.  A Knowledge Representation is an explicit mathematical and algorithmic way of writing all of this out so that it can be broken down into smaller, independent sets of variables.