When an entrepreneur makes a profit, their business prospers.
Prosper is a verb, an action. It means to be successful and growing, usually financially. In this sentence prosper is used to show that the business is doing well and bringing in money.
Profit can be used as a noun or a verb. When used as a noun, profit is the amount of money gained.
For example if I opened a lemonade stand and sold a cup of lemonade for 50 cents and it cost me 20 cents for the cup and ingredients, then my profit would be 30 cents. In order for a business to prosper (be successful), it is important to turn a profit (have more money than is spent).
