One of the most prominent aspects of the Constitution in recent years is the section of the Constitution that allows the President to be impeached. The word impeach simply means charge (an official) with an offence whilst in public office. But it is a highly loaded word, both politically and emotionally. The Constitution actually says nothing specific about under what circumstances anyone can be impeached. It simply defines the final process - that of the trial and penalties.
Article 3, section 2.3 of the Constitution lays down that all crimes shall be tried by jury, except in cases of impeachment and Article 1, section 3.6 provides that only the Senate may try an impeachment. They must be under oath (or affirmation) to do so, and to be found guilty under this process there must be a vote of two-thirds of the Senate. In the event of the President being tried, 3.6 requires that the house be presided over by the Chief Justice, to avoid the conflict of having the Vice President, who would normally preside.
Should the trial be successful, section 3.7 defines the maximum penalties that the Senate can impose. These are limited basically removal from office, and disqualification from holding any official office, although it doesn't preclude a criminal trial.
Article 2, section 4, requires that the President, Vice President, and all civil officers, must be removed from office if they are impeached, and then convicted of, "treason, bribery, or other high crimes and misdemeanors".
So what does all this mean in reality. Well, impeachment is simply the process by which the individual can be charged with an offence - they are innocent until proven guilty. And it also doesn't mean that they will be removed from office. It simply means that they will face a formal trial in the Senate.
Impeachment proceedings can be brought for any offence - there is no requirement in the Constitution that it can only be for "treason, bribery, or other high crimes and misdemeanors"; these are merely the circumstances under which removal from office is obligatory - although, because the process is so cumbersome and time-consuming, it is rarely used and is limited to "treason, bribery, or other high crimes and misdemeanors".
The whole business of impeachment gave those writing the Constitution no end of headaches. There was a strong voice saying that it was unwise to allow the President to be impeached, because it would make him too dependent on the (partisan) legislature, particularly as, at that time, they were the people that elected him in the first place. But Benjamin Franklin disagreed, suggesting that impeachment was better than the alternative - assassination! His view prevailed, although they further struggled over the wording of the conditions for removal from office - in the first draft, it was "neglect of duty, bribery, maladministration and corruption".
States also have impeachment processes built into their local constitutions, and these too provide for removal from office in the event of a successful impeachment. The only exception is Oregon.
There have been numerous examples of the impeachment process - for details see Who Has Been Impeached.