Whether sedentary or nomadic, most Indian nations lived communally. That is, they did not believe in land ownership and generally shared the fruits of their labors. This, of course, was anathema to the American belief in individual property and private enterprise, rooted in the Protestant work ethic.
While some in the late 19th and early 20th century still favored extermination, the growing reform movement in the US at the time pushed for assimilation and guiding American Indians toward full citizenship. The vast number of American Indian boarding schools that spread across the nation represented one aspect of this movement. The other aspect was to encourage American Indians to "take up the plow."
The premise on which the Dawes Act was based came from the Marshall Trilogy wherein Chief Justice John Marshall opined that the US government held title to American Indian land and Indians enjoyed only a right of occupancy. Under the Dawes Act, Congress allotted portions of the reservations that the government owned and the American Indians occupied to individual male Indians in parcels of between 80 and 160 acres--dependent on family status. Indians not living on reservations or whose tribes had no reservation could apply for allotments on lands owned by the US government.
It is important to note here that the government was not "giving" anything away to American Indians. Their land had been whittled down by treaties and encroachment until all that remained were the reservation lands held in trust for them by the federal government. All the government did was to parcel out those lands to individual Indians. These separate allotments were to remain in trust with the government for 25 years after which title would be transferred to the individual Indian or his heirs.
One failure of the General Allotment Act was the inherent belief that American Indians could not run their own affairs and adapt their traditions to reservation life. Another was the failure to follow through with providing equipment and training to enable Indians to gain the most from their land. Worse, the Dawes Act reflects the duplicity with which the US treated American Indians.
All tribal lands remaining after allotment were opened for sale to non-Indians. Proceeds from the sale would be held in trust for the tribe by the federal government "and the same,... shall be at all times subject to appropriation by Congress for the education and civilization of such tribe or tribes of Indians or the members thereof." (1) Theoretically, the tribes had to consent to such sales but pressure from government and abject poverty led to major encroachments. That same poverty and lack of training and equipment caused many individual Indians to sell off their land once they gained clear title. The result was a checker boarding effect that continues to plague Indian nations. The Dawes Act is also behind Cobell v Norton, the decade-long lawsuit over Individual Indian Money Accounts.
(1) See American Legal History-Russell