Unlike a standard rights issue an non-renounceable rights issue is one that cannot be transferred to another investor.
Under a traditional renouncable right issue the holder of the shares as the option to transfer rights to another investor (usually for a price).
This is not an option for a non-renounceable rights issue and the investor has one of two choices
1) Take up the rights
2) Ignore the rights
Neither is necessarily the right option as the decision the investor needs to take depends on why the company has offered the rights in the first place.