The answer by @jwh20 is good but does not summarize the nature of a non-profit organization. There are essentially three kinds of private entities.
- A natural person is a human being who is looking out for him/herself and his/her family.
- A regular corporation has a fundamental goal of making a profit for the shareholders.
- A non-profit corporation has a fundamental goal of serving the community in some way that is recognized by law as a worthwhile charitable service. Examples include feeding the hungry, education, and medical services.
Non-profits may raise money by asking for donations, selling goods (for example bake sales and auctions of donated items), and charging fees for the goods and services that are directly related to their fundamental goals. For example, an ambulance service might be non-profit but still charge for transporting patients to the hospital.
What distinguishes a non-profit from a regular corporation is what happens if they are financially successful. If a regular corporation makes a profit, they pay out the profit to the shareholders. If a non-profit makes a profit, they can use it to expand their operations, use it to lower their prices next year, give it to another charity, or something along those lines. They don't have any shareholders, and are forbidden from giving it to their founders, members, directors, or the like.
A natural person cannot be a non-profit.
I live in the US and my vocabulary is what you will find there. Other countries have similar concepts but may use different words.