Brief Summary
The Set-Up
The government needed some way of obtaining Native American land for all the white settlers that were heading west, while forcing the tribes to assimilate into American culture. They needed a way to do that without looking like bad guys. The Dawes Act, with its misleadingly philanthropic-sounding program of individual land allotments, was the answer.
The Text
First and foremost, the Dawes Act wanted to establish the fact that tribes were going to have to live on designated amounts of land within the reservations. This would not only force them to give up the prime farmlands to white settlers, but it would make it necessary for them to abandon their traditional, communal agricultural methods for the American/European farming model (i.e., for one's own personal profit).
Any land left over after this generous allotment was now available for the government to purchase from the Native Americans, conveniently opening up even more land for the people playing the real-life version of The Oregon Trail.
TL;DR
We're gonna break up the reservation land and give it to individual Native Americans in the hope that they'll become just like the rest of us and give up their primitive tribal ways in exchange for U.S. citizenship. If there's any land left, we'll be happy to take it off your hands. PS: members of the Five Civilized Tribes need not apply.