The New Zealand Electoral Commission gives a brief history of the Maori seats and explains how the system works.
http://www.elections.org.nz/voting-system/maori-representationTo expand on this, based upon books I have read about New Zealand history.
In the 19th century New Zealand started out with a single voters roll, which any British subject who met a landowning qualification could qualify for. In theory the Maori could qualify but in practice few did because the Maori tradition of communal land ownership was incosistent with European ideas about how land could be owned by individuals.
The Maori became discontented over the amount of land settlers had taken over. The Europeans did not realise how discontented until the King Country War broke out. This was a big enough threat to the colony that Imperial troops had to be sent from as far away as India to reinforce the colonial militia.
As an emergency measure, so that the Maori could express their grievances by participating in politics and not have to resort to war, it was decided to create four Maori seats in the New Zealand legislature. This was originally intended to be a temporary measure, but the Maori liked the system and it was made permanent.
The Maori seats elected Maori members to a small legislature, so they could exercise significant political power. This distinguishes the New Zealand practice from that in South Africa, where all the members of legislatures had to be of European descent both before and after communal representatives were introduced into the House of Assembly.
The preamble to the Maori Representation Bill 1867 states:-
http://www.nzlii.org/nz/legis/hist_bill/mrb1867431247/
