If you were trying to open a health/fitness club/busn, what would you write as the purpose for a busn plan?
The purpose of most businesses is to make a profit, writing a business plan helps show you have researched what it would take to do that and show that you project to earn a profit.
Any other answer like helping to keep people fit or other social things are just side effects to making a profit. Without a profit the business will fold.
You need to decide who your target customers are. Curves is looking to serve women with a quick workout and is a different place than a place like Gold’s Gym that is more for male body builders.