pons. 1. any slip of tissue connecting two parts of an organ. 2. that part of the central nervous system lying between the medulla oblongata and the midbrain, ventral to the cerebellum; see brainstem.. [TA] In neuroanatomy, the pons varolii or pons cerebelli; that part of the brainstem between the medulla oblongata caudally and the mesencephalon rostrally, composed of the basilar part of pons and the tegmentum of pons.