Let's take a look at these points in more depth - and just be clear this list is not exhaustive, and most people spend years, if not decades learning how to play the game.
"A business occurs inside of relationships in a group or community"
When you start out in business nobody knows you exist, so developing existence for your business - who you are and what you offer, is vital for your success. If only a few people know you are there, even with the greatest product or service it is really tough to be in business. So what can you do? First, you must choose a community you want to serve and design the experience you want that community to have of you. Next, you need to choose the most effective method of having people find out about your company's existence. If the experience you provide matches that community's expectations, your business has a powerful foundation for success. Second, you require a reliable process to develop relationships. More on this on the next point.
"Business finds out what's needed and wanted"
To truly know what people need and want, you need to ask people key questions about their challenges and opportunities in a specific area of their lives or business. This initiates the process of developing value-driven relationships. As you gather valuable information, and analyse it you will see the situation at hand and discover people's real problems. For your business, the question you will answer is "What is people's unsolved problem? How can my business solve it for them?" For example, in your research you may discover that busy executive's real problem is having more time to spend with family. With that information you can create offers that your market wants. In the case of the executive it could be "Work less and spend more time with your family." If you do this you can truly be of service as a business and be distinct from your competition because you can listen to the real need of the marketplace.
"It produces and delivers upon what's needed and wanted -- and, in the process, solves a problem/challenge of a group or community"
Finding out what is needed and wanted is one side of the coin. The next step of a business is to deliver upon a reliable solution for the problem people are having. This is where the rubber hits the road. If you can deliver you can earn the right to be in business.
"The people that run and own the business ("business people") are remunerated/compensated monetarily for it"
Here's the deal: we all know that we are in business to make money, and you either run and/or own your business - or the business runs and/or owns you. The choice is yours. If you run it and own it, you have a chance to be compensated well and be profitable. If the business runs you, or owns you - just be clear you are not playing the game of business the way it was designed. You are playing the self-employment game which is designed for survival. Bottom line is, you can either choose to get compensated inside of the parameters you determine as an owner/operator or the business will determine it for you. (By the way, if you run and own your business, plan for how you can simply own it, and have others run it for you - and still get compensated for it. The game of business was ultimately designed to be played that way.)
"It maintains the relationships over and over again"
To have your business really make an impact and have ever increasing profitability it needs to continuously invent new offers, products and services for the community it serves. A business has distinct relationships with their buyers and the key distinction is customers versus clients. Many businesses acquire customers who are people that buy from you one-time, whereas clients are multi-time buyers - they are people come back and buy from you over and over again. Ensure you design your business to have clients so that you have stability and ever-increasing profitability as a business.