A market is free if people can buy and sell whatever they want without any interference from a government, and if prices are set by supply and demand. Supply is how much of a product (both goods like Pringles and services like open-heart surgery) is being sold. Demand is how much of that product is being bought.
Supply and demand change when things about the product change, such as its price, its profitability, or its popularity. Lots of people will pay £1 for a tub of Pringles and few people will pay £100, so demand for the crisps goes up when its price goes down. Similarly, if heart surgeon salaries were very low, fewer medical students would specialise in cardiology and it would be harder to find someone to supply you with heart surgery.
Free markets have a strong fanbase amongst economists because they’re often seen as the ‘fairest’ and most efficient way to set prices for stuff. In theory, free market prices rarely rise much above the cost of producing something and therefore stop sellers making excessive profits.
That’s because either nobody will buy an overpriced item or because the opportunity to make big profits will motivate other people to start selling the same thing at a slightly lower price (in order to win customers). The first seller will then have to respond by lowering their price below that of their new competitor(s), who will lower their prices in turn, until nobody can lower the price anymore without losing money.
But this doesn’t always happen in practice. Sellers might strike a bargain to keep their prices at the same high rate (known as collusion). Or becoming a rival seller might be really difficult or take a long time because the item in question requires special skills or technology to produce (called barriers to entry). Or there might be such a limited amount of the product that people will be still be willing to buy it at very high prices.
Even if free markets always worked as they were supposed to, most societies would still prefer for their governments to have some influence over buying and selling. That could be because they think sales of some stuff should be banned (such as heroin or human slaves) or because they want products to be forced to meet certain safety and quality requirements (such as not putting dangerous chemicals in food).
In addition, many of us feel that only certain people should be allowed to buy certain things (adults and cigarettes, say, or cancer patients and cannabis) or that only certain people should be allowed to sell certain things (only those with special training and qualifications being allowed to supply medical services, for example).
Because of this, pretty much no economy in the world has completely free markets. But free-ish markets in places like the UK and the US have been repeatedly praised for vastly improving global living standards by making most stuff cheaper and most people richer. Forbes calls free markets “the most powerful non-religious force for good in the history of the world”.
On the other hand, free-ish markets have been criticised by thinkers like Karl Marx for distributing resources by means rather than need and increasing inequality. A rich, full person might be willing to pay more for those Pringles than a poor, hungry person even though they need it less. That’s why government often decide that it’s in the public interest to forbid some things from going over a certain price (e.g. rent controls) or under a certain price (e.g. minimum wages).
Other common criticism of free markets is that they encourage environmental damage by not pricing in externalities, and that they don’t seem to convince people to buy enough of ‘merit goods’. Merit goods are things like education and healthcare that are useful to individuals and society. A lot of people are completely against selling them in a free market and want governments to fund them instead.