It means the school was formerly private but 'integrated' into the state schools system under a 1975 act allowing them to access greater state funding, whilst maintaining the school's "special character" (usually religious) and still charge fees. They are therefore usually somewhere between state and private schools in terms of cost to parent, resources and facilities, and class sizes. BTW, all schools in NZ get some government funding- even high fee charging ones. Fees for state integrated can range hugely from not much more than "voluntary donations" of high Decile Auckland schools to close to private school fees and they also vary hugely depending on their "special character", etc. I'd advise getting all the info you can and then going to visit each school- ideally with as little notice as possible and spend as long as possible at the school. HTH.