what was the importance of Charles I of England? What resulted from his execution?

Answer 1

"chrstnwr" has part of it above. The English Civil War took place in the 1640s before Charles I was executed (January 1649). It was indeed a battle between a representative government - parliament - of the people (basically just the MEN with property back then) and an absolute divine right monarch. England proved it would not tolerate an absolute ruler. The divine right ruler (Charles I) lost - - and was beheaded to prevent any return to the absolute rule idea.
Even when the republic under Cromwell eventually failed,
the Restoration of the monarchy under Charles II in 1660 included controls on the king's power. England became a constitutional monarchy with a set of rules which the king must abide. This whole process had actually begun in England as far back as 1215 with the Magna Carta spelling out the things the king could not do. England was one of the first European countries to discard absolute monarchy as a system of government (the Netherlands being the other).
That is the significance of Charles I's death - - a definitive change in the political system of England (later Great Britain).

Answer 2

Charles I wanted to be an absolutist monarch and ignore what Parliament said about it.

The result from his execution was the English Civil War and the Restoration Period.