As a member of the military, Jackson was involved frequently in skirmishes and outright battles with tribes of Indians who were trying to drive the invaders out of their territory. Jackson and others in the Tennessee militia and the United States Army did not agree with the Indian's interpretation of the situation.
Jackson battled Creek Indians near Fort Mims, north of where Mobile, Alabama is now located, after warriors attacked the fort. Jackson led a larger force against Creek warriors at Horseshoe Bend on the Tallapoosa River in Alabama, killing 900 and taking 300 prisoners. His battles and victories against the Indians made him a hero among settlers eager to expand into the rich new territories that had been occupied by the natives.
As your quote reflects, Jackson's conclusion was that the only way to prevent continual warfare was to completely separate the area occupied by the Indians from the part of the country settled by those of European ancestry.