Johnson did fire Lincoln’s Secretary of War Edwin Stanton and replaced him with a very reluctant Ulysses S. Grant, former commander of the Union forces.
The Tenure of Office Act gave Congress a power that goes beyond its constitutional power of advice and consent in Presidential appointments. The T.O.O.A gave congress the same power with regard to cabinet members whom Johnson sought to fire – no one can be fired without the consent of Congress.
This was basically a battle between a southern-born President and the radical Republicans of the north who controlled congress and hated Johnson. The end result was Johnson’s impeachment and near conviction. The Act was eventually found unconstitutional by the Supreme Court