To fill out bibliophage
's explanation, Article I, which describes the Congress, provides in section 2 that "The House of Representatives . . . shall have the sole Power of Impeachment." Article I provides in Section 3 that:
The Senate shall have the sole Power to try all Impeachments. When sitting for that Purpose, they shall be on Oath or Affirmation. When the President of the United States is tried the Chief Justice shall preside: And no Person shall be convicted without the Concurrence of two thirds of the Members present.
Judgment in Cases of Impeachment shall not extend further than to removal from Office, and disqualification to hold and enjoy any Office of honor, Trust or Profit under the United States: but the Party convicted shall nevertheless be liable and subject to Indictment, Trial, Judgment and Punishment, according to Law.
Article II covers the Executive power of the United States. It provides in Section 4 that:
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.
Putting it all together, any civil officer of the United States, from cabinet secretaries to third assistant agriculture inspectors may be impeached by the House of Representatives and tried by the Senate. If impeached and convicted, the officer may be removed from office, and may further be disqualified from holding any federal office of honor, trust or profit, but that's it. The officer may also be indicted, tried and punished according to the ordinary criminal law.
Under Article II, Sec. 4, the impeachment and conviction must be for "Treason, Bribery, or other high Crimes and Misdemeanors," but whether a particular misdeed fits into the impeachable category has been held by the Supreme Court to be a nonjusticiable political question. See Nixon v. United States, 506 U.S. 224
(1993) (affirming the removal of a federal judge). What this means is that "high Crimes and Misdemeanors" effectively means whatever Congress finds it to mean by impeaching and convicting someone.