Supply-side economics was started by the the Wall St. Journal opinion editor, Robert Bartley and his right-hand man Jude Wanniski. They worked with two economists, Author Laffer and Robert Mundell. But Bartley took the lead, and much of supply-side economics was developed by him and Laffer at a series of dinners at Michael I a posh restaurant a few steps from Wall Street.
They viewed it as an attack on Keynesian economics, which described how to get out of a depression by having the government increase demand for goods and services from the private sector. This is how we got out of the Great Depression during World War II (though Keynesian economics does not suggest war as even a possible policy measure). Since Keynes focused on the demand side, Bartley and Laffer focussed on the supply side (remember "supply and demand") and call their theory "supply-side economics."
In a nutshell, Keynesian (demand-side) economics, says that when a country is in a recession, it's because businesses don't have enough business. That is, people are not buying as much as usual, so they can't sell enough, so they lay people off, and then the people who are laid off, or are afraid of being laid off, buy even less. To get things going, we need something to increase demand. Conservative economists tend to say -- have the Fed reduce interest rates so people and businesses will borrow and spend more. Liberal economists tend to say have the government cut taxes for the poor, because they will spend, or have the government borrow and spend more to help business get started again.
The right answer, is that in a regular recession, monetary policy works and is much easier to use so that is best. But in a terrible recession or a depression, the interest rate goes down to about zero and can't go any lower, so then monetary policy stops working. Then you need Keynesian economics -- like the spending for World War II>
Both conservative (monetarist -- like Milton Friedman) and liberal (Keynesian) economists say that the government needs to stimulate demand in a recession. But the two "supply-side" economist say both are wrong, that we need to give tax cuts to the rich and then the rich will be stimulated to work much harder and they are the ones who are most productive and that will make the economy hum again. Laffer drew his famous "Laffer curve" to try to prove this point (but it is just plain silly). It claims that if the government cuts their tax rate, the rich will make so much more money that they will pay more taxes not less. It also claims that if you cut the tax rate for the bottom 98% of the population this won't happen.
So this was tried under Reagan. Big tax cuts for the rich. And G. W. H. Bush called this "voodoo economics," because only two economists believed it (or at least they often said they did), and because the idea that cutting taxes for the rich would collect more money not less. Of course it never worked, and that's one reason the Supply Siders ran up the debt (even compared to GDP) for 20 out of 20 years, while other Presidents, both Republicans and Democrats did not have this problem.