The New Zealand accent is often described as similar to Australian and South African English. The sound of an accent is perceived differently depending on the linguistic background of the listener. Most dialects of English tend to differ most in their pronunciation of vowels and diphthongs, which are vowel combinations.
One of the most obvious differences is the pronunciation of the vowel sound /i/, which is pronounced as a schwa, meaning words like "bed" often sound like "bid." "Really" and "rarely" are pronounced almost the same, and "pull," "pool" and "Paul" are very difficult to distinguish. There are many resources with examples of the New Zealand accent available, and it is helpful to seek an audio example.