When the Constitution was being written, there was a big concern that the government or some of the people in the government would have too much power or would abuse the power they had. To deal with this possibility, the Founding Fathers made it possible to impeach a person such as the President if he broke laws or was accused of misconduct in office.
In our system, the legislative branch would handle the impeachment process. The House of Representatives would determine if there is enough evidence to impeach the President. If the House of Representatives impeaches the President, then the Senate would conduct the impeachment trial. In order to remove the President, two-thirds of the Senate must vote to convict him.
There have only been two presidents that have been impeached. These presidents were Andrew Johnson and Bill Clinton. Neither person was removed from office, although Andrew Johnson fell one vote short of conviction.
The legislative branch is responsible for the impeachment of a President.