So why is what I buy and sell anybody else’s business? The thing is, pretty much nothing happens in isolation—everything will have a spillover effect of some kind, good or bad. That’s when it becomes everybody’s business. Some economists call these spillover effects "externalities", because it's a decision that affects more people than just the buyer and seller (the effect is external to the exchange), but isn’t reflected in the price.
A classic example of a negative externality is pollution. A company buys electricity from a coal-fired power plant at a certain price based on how much they need that electricity. What’s not included in the price are the toxic chemicals breathed in by anyone unfortunate enough to live close by.
So who pays them back for the inconvenience? No-one, probably, because they never asked to have a power plant there in the first place, so weren’t at the negotiation table when the price was set. Instead, governments often step in, to place restrictions industries that are likely to have spillover effects people don’t want.
What about a positive externality? Take education. In one sense, it’s an exchange between a school and a student. But anyone who comes into contact with an educated person can benefit from their knowledge in some way, even though they didn’t pay for them to get it. Because the value of their education spills over far beyond the student themselves, some economists argue that a purely private school system would under-invest in education because each family would only consider the benefits to their child, rather than to society as a whole, when putting a price on the value of their education.
Why does all this matter? Basically because it’s another way people justify why they think certain things should be public and others private, or certain industries regulated and others not. Rather than focusing on the question of what’s more efficient, it’s focusing on what’s fair to everyone involved.