A non-renounceable rights issue refers to an offer issued by a corporation to shareholders to purchase more shares of the company (usually at a discount).
Unlike a 'renounceable right', a 'non-renounceable right' is not transferable, and therefore cannot be bought or sold.
Why do companies issue rights?
Issuing more shares dilutes the value of outstanding stock. However, a rights issue allows the existing shareholders to buy the newly issued stock at a discount, meaning they are compensated for the impending share dilution. The compensation the rights issue gives them is intended to be equivalent to the cost of share dilution.