When something is prospering, it's profitable, or making money. The busy little bookstore downtown seems like a prospering business — especially since the huge chain store closed last year.
Anything that's prospering is successful, particularly in an economic sense. A prospering restaurant is full of happy diners every night, and a prospering lemonade stand is doing a booming business, its cash box overflowing with dollars. Prospering is from prosper and its Latin root, prosperus, "favorable or fortunate."