The region of a plant that produces cells is called the meristem.

There are two main types of meristem:

* Apical meristem: Found at the tips of roots and shoots, responsible for primary growth (elongation of the plant).

* Lateral meristem: Found in the vascular cambium and cork cambium, responsible for secondary growth (increase in girth of the plant).

So, while there are many regions in a plant that have specific functions, the meristem is the one that's solely dedicated to cell production.