When the GDPR can apply to a business here
The GDPR applies to organisations established in the EU. Article 3 of the Regulation also extends it to organisations outside the EU in two situations: where they offer goods or services to people in the EU, or where they monitor the behaviour of people in the EU, for example through tracking on a website.
Offering goods or services means more than having a website that Europeans can visit. The Regulation's recitals point to signs that a business is targeting people in the EU, such as using a European language or mentioning customers there, and in practice shipping to EU countries or advertising aimed at EU audiences point the same way. A Wellington software company selling subscriptions to customers in Germany is in a very different position from an Auckland café whose website a tourist once read.
Other ways the GDPR shows up
Even where the GDPR does not apply to you directly, it can arrive through contracts. A European customer or partner that is subject to the GDPR may require you to sign data processing terms before it sends you personal information. If you provide services to such a business, those terms are often non-negotiable, and you will need to be able to show how you handle the information.