Impeach means to charge someone with doing something wrong, specifically a high government official, such as the U.S. president, a senator, or a federal judge. Fortunately, very few presidents have had the dishonor of being impeached.
If you impeach a president, you charge him or her with a crime. Congress may vote to impeach a president, but being impeached is only the first step in removing an official from office. Impeach comes from the Latin impedicare, meaning "catch, entangle." To impeach also means to cast doubt on someone's character. In a courtroom, a lawyer could impeach the credibility of a witness in order to discredit whatever that person said.