Famously dubbed "voodoo economics" by George Bush (father), supply side economics is associated with the Laffer curve describing taxes. But neither voodoo nor taxes obviously have to do with supply - so why the "supply side" in "supply side economics"?
To understand this, we need to go back to basic economics: supply and demand. The supply curve slopes up: with increasing price, the amount produced - the supply - goes up. The demand curve slopes down: increases in price discourage consumption, decreasing demand. Where the two lines cross marks the actual quantity of goods produced and consumed, and their price. This gives us the following graph:
Now, let's suppose the government uses one of the classical Keynesian methods to stimulate the economy, by spending more money without raising taxes, and monetizing the resulting debt by essentially printing money. The additional government purchases stimulate demand, moving the demand curve curve up and to the right. This has the effect of increasing the total quantity of goods and services produced and consumed - the objective of economic stimulus:
From this graph, you can see another effect of government attempts to stimulate demand: the price goes up, as well as quantity.
Viewing this keynesian stimulation from a monetarist point of view, this is because of the increase in the money supply from monetizing the debt created by the increased spending. That increase in money supply goes partly towards increasing the quantity of goods and services produced and consumed, and partly towards increasing their price.
Of course a monetarist would point out that you could get the same effect by increasing the money supply, even without the extra government spending. And to the extent that price stability is desirable, the inflationary effect of demand side stimulation would require that monetization of the government debt - such as by the central bank buying government bonds - would need to be compensated by contractionary monetary measures elsewhere, which would tend to counteract the beneficial effect of the stimulus on the size of the economy.
Now let's look at what happens when the government uses the other classical Keynesian method of stimulation, which is to reduce taxes rather than to increase government spending. In particular, let's suppose that the reduction in taxes is from a reduction in the tax rate on labor, the primary input to a modern economy, with the result that each dollar actually paid to the laborer has a smaller tax overhead, and thus a smaller overall cost. As with the previous case, the debt is monetized by printing money. This stimulus works on the supply curve, rather than the demand curve:
Again, the total quantity of the goods and services produced and consumed is increased. But this time, prices go down - the effect is deflationary, rather than inflationary. Price stability concerns now dictate that, instead of compensating for inflationary stimulus with contractionary measures, the central bank must "compensate" for this deflationary stimulus with additional expansionary measures, which will further boost the economy! This is the "voodoo" part of "voodoo economics".
But what happened to the original monetary expansion that was used to finance the debt from cutting the tax rates? It turns out that monetary expansion does the same thing as it did with demand side stimulus: it goes partly towards increasing the quantity of goods and services produced and consumed, and partly towards increasing their price. However, this price increase is more than offset by the direct price reduction of supply side stimulus. These two components of the price and quantity movements result in the net effect of stimulus with a price reduction:
This is what supply side economics is all about: manipulating the supply curve, rather than the demand curve, to maximize the economic stimulus consistent with price stability.
U.S. per capita GDP, 1871-2009; contrast the effects of demand side stimulus in the 1930s with supply side stimulus in the 1960s and 1980s: