I know foliations as a particular topic in differential geometry. I understand the definition and basic properties of a foliation from the DG point of view, including the Frobenius theorem. While trying to understand why this concept is important I came across this Wikipedia page on integrability conditions for differential systems, but couldn't understand much of it. I do not want to too diverge from my other studies now, yet want to understand this association quickly and completely.
Can you suggest me a source that is solely focused on the relation between foliations and systems of PDEs?