When the Civil War was over, the South was certainly conquered, but the nation was still politically divided in two. With Lincoln dead, Congress broken into two distinct camps on how to reunify the country. There was Lincoln's 10% Plan, which said that if 10% of the number of people who voted in the 1860 swore allegiance to the Union, then the state could be readmitted and send Congressmen and Senators to Washington DC, just like nothing had happened. The whole purpose of the war was to reunite the country, so Lincoln wanted to make it as easy as possible.
By contrast, some of the more radical Senators hated the South, and wished to punish it for secession and the war. Thaddeus Stevens proposed the Conquered Province Theory, which said that the South shouldn't be readmitted at all, but run like an occupied state, divided into 5 military districts and administered by the Union Army.
Luckily, cooler heads prevailed and Lincoln's plan was adopted.