The above answer isn't very accurate.
Supply side, or classical economics and Keynesian and New Keynesian economics are two very important ways of modeling the world, but with very different assumptions. They are both correct modeling methods, but in the circumstances classical economics works, the Keynesian fails. In the case that the Keynesian is operative, the classical fails. They cover non-overlapping circumstances.
The idea of both starts in the labor market. Imagine that the US economy's labor supply and labor demand meet at the point of 4 billion hours of labor a week.
Under the classical assumptions, people are paid the "marginal product" of their labor. Or, simplified, the real wage is competitively set and in aggregate can fluctuate.
This real wage, not the nominal wage you get paid, but its value in terms of goods and services then maps onto a "production function." Simplified, this is just the output of the labor and the capital employed. The reason we do not discuss the capital is that it is assumed that employers try and make rational allocations between machines and people where they can and that they learn from their mistakes. Further, a dollar is a dollar and the market for capital is very competitive. Labor is less so. Further, it is thought that people would prefer leisure to working, but machines of course do not care. Companies can make mistakes, but the assumption is that they learn from them.
The assumption of the production function is that the more hours a person works, the more tired they get and so the less effective they become. Likewise, the harder you work a machine the more likely it is to wear out and so adding hours doesn't automatically add much output.
This is the supply side. The output is determined by the costs and the producer will demand as much labor and capital as it can until the marginal product of capital equal the real wage and the real return on investment of the capital.
This is very important because when classical models are operating only supply matters. Classical models operate under normal conditions in the US economy and always operate in the long run. A way to think about this is that, in the short run, if a producer believes that they can produce 10 tomatoes and that any after that reduces profit, they will produce 10 tomatoes. If you were the sole consumer of tomatoes and wanted to buy 20 tomatoes, you cannot. You cannot buy something that does not exist.
So demand matters in setting the ultimate price, but demand has no impact, from a policy maker's perspective, in determining the national income, wage or unemployment. The only useful thing you can do is try and make the economy more flexible and encourage technological change to improve the national income and employment.
Keynesian economics acknowledges that in times of stress, the economy stops behaving in a flexible manner and that changes in demand then in fact can determine supply issues.
For example, if you set a fixed minimum price for goods, such as in price controls and the price is above the price the market would pay under a free and flexible system, you reduce output because sellers cannot produce as much as they wish because people will be unwilling to buy it. If you put out 10 tomatoes only 8 will get eaten and two will rot because the price is too high. Knowing this, farmers will then lay off farmworkers reducing real wages far in disproportion to the shift, making everything much more expensive while dropping real wages.
This is happening right now in Indonesia and it has pushed 5 million people into poverty. They passed farm price controls to keep farmers from failing raising the price of food while cutting wages forcing people into starvation, while protecting farm owners from being forced to close.
Likewise, fixing the minimum wage above the market clearing wage forces producers to pay more than the marginal product of labor. It would be like having an employee that produces goods that a store's customers will pay $7 for, but requiring a wage of $7.50. So the employer reduces employment either substituting capital or simply ending lines of business that require low skill workers. In Keynesian economics, due to the level of competition for work and capital, those low value services just get shipped overseas to a place without a minimum wage.
So Keynesian economics explains how rigidities in the economy impact everything else. So if you set a minimum wage or a minimum price or a maximum interest rate, it describes what will happen to the rest of the economy.
Keynesian economics comes out of the Great Depression. During the Depression, wages did not fall even though prices did. As a consequence, everyone who was still employed, in effect, got a large pay raise. However within one year 25% of workers lost their jobs. Only high value workers were able to keep their jobs. Rigidities occur naturally to some extent, but it is a bad idea for a government to purposefully create them.
Rent control, minimum wages, regulated interest rates are all bad ideas if your goal is to make the nation as well off as possible. They also do not really help the poor unless they are very short term measures. They probably make the poor even more poor.
By the way, this is the problem behind nationalized medicine. If you lose market conditions you cannot see price signals. If you cannot see price signals you cannot know how valuable a service really is to the public. Likewise, you cease being able to know what to pay a physician or a nurse. Markets send signals and price is used as the rationing tool.
The real reason we have a health care crisis is that we have a shortage of doctors and nurses. We are getting fatter, demanding more medicine and boomer doctors and nurses are going to be retiring soon. When you see large price shifts you are in a shortage situation. If you want to solve the health care crisis, you need to drive down the cost of medicine. You can only do this by adding to the supply of nurses and physicians. You have to incentive people who would otherwise be biologists, psychologists or engineers to enter health care to add supply and thereby reduce costs.
If we nationalize health care, we will create a Keynesian situation and you will see the crisis become even more acute. You will either have more rationing than we already have, you will overpay the doctors and make it even more expensive than it already is and not treat any extra people, or most likely you will drive physicians into other professions skyrocketing costs and reducing care substantially.
If costs fell, the insurance issues would go away. You have to add to the supply AND/OR improve American health to reduce the demands on the system.
I am an economist.