The Constitution states "The President, Vice President, and all civil officers of the United States" are subject to impeachment. Who are "civil officers"?
Historically, civil officers who have been impeached are judges and cabinet members. William Blount, a U.S. Senator from Tennessee was impeached in 1797 but the Senate dismissed the charges, deciding that Senators cannot be impeached.
Impeachment does not automatically remove someone from office. Following impeachment proceedings in the House, a trial is held in the Senate (assuming the person in question doesn't resign first).
In the event of a Senate trial, someone may be found Guilty, Not Guilty, or have the charges dismissed.