The phrase "to jump through hoops" means to go to a lot of trouble or effort for someone, often by performing tasks that are difficult or time-consuming. It is an idiomatic expression used to describe doing something that requires a great deal of work and energy in order to please another person or satisfy their demands. The phrase originated from the practice of circus performers who had to jump through small hoops held by trainers, as part of their training routine. Today, it is commonly used figuratively to describe any situation where someone has to do a lot of work in order to achieve something.