You didn't play Colonization to death like me (us?) if you can't understand the use of Peter Minuit.
Thing is, Peter Minuit is only useful if you plan to play a peaceful type of game. If you do (and the French are great at this), then Peter Minuit becomes almost absolutely necessary because otherwise you'll have to pay for land. Land which will either be taken by force, greatly alarming the Natives, or purchased with money you can't afford to spend in great quantities or at all.
The great power of a peaceful game with the Native come with trading wagons in mid and late game. By specializing a town in production of refined goods, instead of splitting it half and half with base resources, and by trading with the nearby native villages, you can up your production at least twofold
and make more money in the process (from trading other goods with the Native to get your base ressources). Add to this a good trade wagon network between your own cities, and you're in business. This process can continue forever as long as you have the goods the Native are asking in exchange, and in late game you simply sell the same goods to the custom house for more profit.
The second great advantage of having good relation with the Natives is that they will help you defend against the Royal Army when you declare your independence. If you are like me then you probably will trade plenty of muskets (that you produced yourself) and horses (that you bred yourself too) to the Natives for ridiculously high prices. Once this is done, the Natives are able to breed their own horses and use the muskets you sold them about as efficiently as any other power... And they get in the way of the Royal Army quite nicely if they are in sufficient numbers.