Why do plants have pith and how is it useful to them?
The pith (medulla) forms part of the ground tissue system of a plant, and specifically it is the ground tissue which lies interior to a plants vascular tissues (xylem, phloem etc.)

The ground tissue system is responsible for much of a plants metabolic functioning, and contains various specialized cell types which aid in photosynthesis and storage of photosynthesis products. The pith is made from parenchyma cells.