One purpose for cell division is tissue repair. For example, when the epithelium that makes up the skin (the epidermis) is damaged, the cells of the stratum basale (the deepest layer of the epidermis) must divide to repair the wound, even if it is superficial (described here).
When there is a superficial wound, the cells of the epidermis are damaged and must be replaced. In the epidermis, only cells of the stratum basale are capable of cell division. These cells migrate to fill in the gap created by the wound. The cells then begin to divide to produce cells that have been damaged in more superficial layers of the skin.
Some cells in the body are not capable of cell division. These cells include neurons of the central nervous system (CNS). Although recent research has provided promising results, in general neurons of the CNS are not capable of division or functional repair making damage to these tissues irreversible in many cases.