Any activity designed to develop or hone a skill or ability.

“The teacher told us that the next exercise is to write an essay.”

Activity intended to improve physical, or sometimes mental, strength and fitness.

“I do crosswords for mental exercise.”

A setting in action or practicing; employment in the proper mode of activity; exertion; application; use.

“The law guarantees us the free exercise of our rights.”

To exert for the sake of training or improvement; to practice in order to develop.

“to exercise troops or horses;  to exercise one's brain with a puzzle”

To perform physical activity for health or training.

“I exercise at the gym every day.”

To use (a right, an option, etc.); to put into practice.

“She is going to exercise her right to vote.”