During the civil wars there were 2 parties: the royalists (supporters of the king, church of England and catholic nobility) and the parliamentarians (supporters of the parliament, mainly puritans).
The royalists were called cavaliers and were mostly gentry, nobility andclergy.
Parliamentarians were called roundhead because they cut their hair very short. Merchants and middle classes sided with them.
The war lasted 7 years, until Cromwell's formation of a special body, the Ironsides (a cavalry regiment).
Once the parliamentarians had won the war, they executed the king after anunjust trial in 1649 and exiled his son.
After his death, the monarchy and the house of lords were abolished and the country was ruled as a republic, known as "commonwealth".
The country was now governed by the house of commons, which means there was a parliament made up of only one chamber (called the rump*). In 1653 the rump gave the power to Oliver Cromwell. The rump was dismissed the same year and Cromwell became lord protector of England and Ireland (he was offered to became king but refused)
* the small or unimportant part of a group or an organization that remains when most of its members have left.