Impeachment is a trial held before Parliament of someone who is charged with a crime against the State. It is usually a charge against a public official.
In the past English custom was for the impeachment to be made in the House of Commons and for the trial to be held in the House of Lords. The first impeachment in this country was of Lord Latimer in 1376, and the last Lord Melville in 1806.
However since 1805 parliamentary procedure has changed. The Cabinet is responsible for the actions of Ministers and Ministers are accountable to Parliament. Their work is scrutinised and they are questioned regularly by Parliament. There is therefore no need for impeachment.
In America public officials may still be impeached. This includes the President. President Clinton was impeached and acquitted in 1999.