A President of the United States can be impeached and removed from office for things such as Treason, Bribery, or other high Crimes and Misdemeanors.
The president has to go through court and be convicted of those things before they can actually be impeached and removed from office.
For example President Clinton was impeached on December 19, 1998, by the House of Representatives on grounds of perjury to a grand jury (by a 228–206 vote) and obstruction of justice (by a 221–212 vote.
The charges of High Crimes and Misdemeanors that a President can be impeached are things such as allegations of misconduct by officials, such as dishonesty, negligence, perjury of oath, abuse of authority, bribery, intimidation, misuse of public funds or assets, failure to supervise, dereliction of duty, unbecoming conduct, refusal to obey a lawful order etc.