One thing I always notice when I'm hearing Kiwis speaking English is the fact that almost every vowel turns into /ɪ/. Here's a video which illustrates the point (listen to them when they speak vowels).
Example words that video whose vowels I hear changed:
Has (sounds like 'his'), neck (nick), men (min), death (dith), centre (cintre), yanked (yinked), says (siz), said (sid), etc.
How did this vowel change come about? It doesn't even seem to exist in Australian English, and it seems rather unhelpful as I find this pronunciation makes many words harder to understand.
Best Answer
They're not all like [ɪ]. They're just different from other dialects. The "vowel" section of the Wikipedia article about New Zealand English discusses how New Zealand vowels are different from other dialects.
Note, however, that /ɪ/ itself is pronunced [ʌ], that is, "sin" sounds almost like how I would say "sun".
As for why, nobody quite knows where sound changes originate. In many languages, including various times in the history of English, when one vowel changes, many others change as well, to redistribute them throughout the vowel space. Such groups of changes are known as chain shifts, the most famous being the Great Vowel Shift. This is clearly what has happened with short vowels New Zealand English. The description in the Wikipedia article says "The short-e /ɛ/ of YES has moved to fill in the space left by /ɪ/, and it is phonetically in the region of [ɪ]", implying this is a pull-chain—a shift of one vowel opens up room in the vowel space that other vowels move into.
I don't know if there are any studies that show the history of the New Zealand vowel shift, so I can't be sure the implication from Wikipedia is correct, as it is uncited, but it is certainly a plausible explanation.