Screamed by little children at one another in the playground, and is presumably a rudimentary accusation technique.
The connection between lying and burning pants is not entirely clear, as cases of spontaneous human combustion aren't generally linked to pathological liars as this remark would suggest. I suppose variants such as "Liar, liar, nose is growing and is made of wood" lack the compactness and style that makes this particular remark so popular.