“Trickle-down economics” is a perjorative term for supply-side economics, which is largely in contrast to “demand-side” economics (also known as Keynsian economics).
The basic idea behind trickle-down economics is the assumption that putting money into the hands of the people who are most likely to make rational investments (that is, investors and businesses) will result in the greatest good to society. It’s argued that people who are investing their own money are most likely to make the soundest decisions that create the most wealth. The “trickle down” part (criticism) comes from the assumption that in creating wealth through successful investment, jobs will be created that benefit people who need to work for their living.
The criticism of this theory is based on the assumption, criticized as elitist, that investors and business owners are wiser and more rational than other people.
There are several versions of “supply side economics,” which can be attributed to economists like Friedrich Hayek and Milton Friedman.
In contrast, Keynesian economics argues that overall economic activity, and the jobs that it creates, rely on demand for goods and services. Keynesians argue that no matter how much money business has, if there is no demand for goods and services, the economy will grind to a halt. In times of economic downturn, Keynesians argue for government spending, which they posit will increase demand overall and get the economy going.
Criticism of Keynesian economics arises from its lack of consideration of whether or not money is used efficiently. To quote one criticism, a Keynesian would think it valuable if the government paid some one to repeatedly bury and unbury bags of money.
John Maynard Keynes and Paul Krugman are well-known economists of this type.