"Compulsory" means "required". In a compulsory dance, also called a pattern dance, you are told exactly what steps you are required to do. The name "compulsory dance" just is a description of what the dance is - one where the skaters do the required steps.
"Original" means you made it up yourself. The original dance was still a kind of pattern dance, but instead of doing required steps, the skaters got to make up the steps themselves. They made up their own pattern, and could skate it over and over. Other people could learn it, too, if they wanted, and sometimes a dance that started off as someone's original dance ends up getting added to the list of compulsory dances.