The original Rump Parliament was the remnant of the Long Parliament, following Pride's Purge (1648). This parliament ordered the execution of Charles I, abolished the monarchy and House of Lords, and formed the Commonwealth of England (1649). The Rump was dissolved by Oliver Cromwell in 1653 when it failed to meet his expectations, and was replaced with the "Barebones Parliament".
The Rump was recalled by Cromwell's son, Richard, after he was appointed Lord Protector in 1658. It demanded his resignation, which was readily obtained.
The word "rump" normally refers to the back end of an animal; its use meaning "remnant" was first recorded in the above context. Since 1649, the term "rump parliament" has been used to refer to any parliament left over after the true parliament has formally dissolved.