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Johnson was impeached (the term being the equivalent to "charged") essentially for his efforts to undermine Congressional policy. The whole process was controversial because under Article II of the United States Constitution (Section 4) "The President, Vice President, and all civil Officers of the United States shall be removed from Office on Impeachment for, and Conviction of, Treason, Bribery, or other High Crimes and Misdemeanors." It is doubtful that any of the allegations made against Johnson properly fell under any of these headings. The Impeachment was the culmination of a lengthy political battle, between Johnson and the "Radical Republican" movement that dominated Congress and sought control of Reconstruction policies.
Johnson was impeached on February 24, 1868 in the U.S. House of Representatives on eleven articles of impeachment detailing his "high crimes and misdemeanors". The main charge against Johnson was a violation of the Tenure of Office Act, passed by Congress the previous year. Specifically, Johnson had removed Edwin M. Stanton, the Secretary of War (whom the Tenure of Office Act was largely designed to protect), from office and replaced him with Ulysses S. Grant. It seems bizarre today to think that a President could be convicted of "high crimes and misdemeanors" for wanting to replace a member of his cabinet.
The articles of impeachment were approved of by the House of Representatives on March 2, 1868 and Johnson's trial began three days later in the Senate, with Supreme Court Chief Justice (and former Secretary of the Treasury) Salmon P. Chase presiding. The trial concluded on May 26 with Johnson's acquittal, the final count falling one vote shy of the required tally for conviction.
The impeachment and subsequent trial has been criticized by many subsequent historians as an act of political expedience, rather than necessity based on Johnson's defiance of a piece of legislation that was repealed in 1887. In 1926 the US Supreme Court expressed an opinion that the Tenure of office Act was an unconstitutional piece of legislation.
There was only one other instance of impeachment of a president, that being of Bill Clinton on December 19, 1998. The story of Johnson's impeachment is told in detail in books such as David O. Stewart's 2010 book Impeached: The Trial of Andrew Johnson and the Fight for Lincoln's Legacy and also in The Impeachment of Andrew Johnson by Chester Hearn (2007).