Intensive active and passive stems
As the qal and niphal go together as active-passive counterparts, so too the piel and pual. The difference is that the meaning is not merely simple, but intensified.
For example, take the verb פָּתַח. In the qal, this word means simply to “open.” However, it is also used in the piel where it can mean to “unstrap” (an animal that is bound, or the sackcloth around your waist, or your armor) or to “unlatch” a door or even to “free” a prisoner. In all these cases, the base meaning “open” is being intensified and hence the piel stem was used.
That being said, how intensive a meaning has to be so as to justify the piel over the qal is inherently subjective. Thus, not too much should be read into a piel stem, especially if the same word does not appear in the qal as well. In addition, the piel will sometimes be extra intensive and carry a causal meaning—something typically reserved for the hiphil stem. For example, the verb שָׂמֵחַ means to “be happy” in the qal, and to “make someone happy” in the piel.
Let’s take a look at a verb commonly appearing in the piel and pual, כָּפַר.