A petiole is a type of stalk that connects leaves on a plant to a central stem. Like, the stem typically grows up, petioles grow out of them, and have leaves directly attached. They're the little "stems" on leaves. (Though they're actually stalks, not stems.)
The petioles we eat are going to be large and crunchy. Given they are not botanically fruits though, they will not be fruits culinarily.