There are several reasons someone might choose to hike in gaiters, here are some of them:
When hiking in the snow or cold alpine conditions gaiters are strongly advisable. They will help to stop snow, ice or water entering the top of your boots and causing your feet to get cold and increase the risk of frost bite. They will also provide some protection to you lower legs when walking through icy knee-deep snow. If you are wearing crampons, they will also offer some protection from cutting or grazing your legs from the points on the crampons.
A pair of gaiters teamed up with the right pair of boots, in certain conditions might keep your feet dry a bit longer. Obviously full-length gaiters (to the top of the calf) and waterproof boots will be much more effective than ankle length puttees and a pair of lightweight non-waterproof boots or shoes. Its handy on trips where you may just have easy, shallow (below gaiter height) river crossings and you don’t want to either a) take your boots off at each crossing or b) walk all day with wet feet. You might need to adapt your technique a little for these crossings, a little bit like a Pukeko in the swamp – take quick and high steps so the water does not have time to find a way in!
Is there likely to be a lot of gritty material, thorns, prickles, small stones or sand? Gaiters will protect your lower legs. Note these sorts of conditions are not typical on your average NZ trail.
Gaiters are a great idea in the mud. It keeps the squelchy stuff out of your boots and will protect your socks too. If you are heading off to Stewart island or the Dusky track take note!
This is by no means an exhaustible set of reasons but it may help you decide whether you strap on a pair before your next hike.