New shorter domain names will be up for grabs from the 30th of September. The change means you'll be able to register .nz domains without the '.co' or '.org'. As an example you could have anyname.nz as well as, or instead of, anyname.co.nz. Benefits include shorter domains and more choice.
If you've got a .co.nz or a .org.nz nothing will change with your existing domain, but you might like to secure the shorter version of your name before anyone else does. Depending on when you domain was registered you might be able to get Preferential Registration Eligibility, giving you first dibs on yourname.nz.