Grant's presidency is usually a compared (unfavorably) to his time as General during the Civil War. It may be true that his presidency didn't live up to his military brilliance, but he did one very important thing that his predecessors were unwilling or unable to do.
Grant came in to power at a time when the KKK was at the height of its power during the reconstruction era. Intimidation, rape and murder of blacks and Whig politicians was commonplace and was out of control.
At this time, many of the vigilante groups acted with impunity and did whatever they could to make life the way it was before the war. Blacks in the south were hated more than ever after slavery by poor whites who viewed their place in life as sinking while the freedman's life was rising.
Grant sent the federal troops in to areas that the KKK/southern militia was occupying and actively fought them. He also sent federal troops in to areas where blacks were being denied the vote and protected them to at least a minimal degree.
The problem with his predecessors after the war was that they followed a policy of appeasement. The south was allowed to go on as if nothing had ever happened in an effort to restore national unity. This accommodating policy brought into question what the war was even fought for. Laws would go on the books giving rights to blacks, but they were still in virtual slavery.
Only by showing resolve did Grant make the violence in the South decline somewhat. This relative peace allowed the country to start on the long road to normalcy before the next national crisis.