The English Civil War was between Parliament, lead by Oliver Cromwell, and the Royalists, who were lead by Charles I. It all started after Charles was trying to implement his "personal rule" and disbanded Parliament. But Parliament was in control of the money, and Charles eventually needed some, so he brought them together again. But if you had been disbanded for eleven years for some reason by a ruler you already didn't really like, you would have some complaints. Parliament had just that.
It was called the Great Remonstrance and was a list of grievances against the King, all for his different faults.
The result of this was Charles raised his banner and declared war on the Parliamentarians. Charles was beaten, and escaped to Scotland. But the people in Scotland turned him in, and he was later executed, making Cromwell the "Lord Protector" of England. This eventually deteriorated, and Parliament invited Charles II to be king.