The danger of irrational exuberance is that it doesn't last. The frenzy of greed then turns to the panic of fear, which drives investors to sell at any cost. This collapse in stock market prices can spread to the entire economy.
Greenspan was talking about the proper role of monetary policy, which usually doesn't concern itself with the stock market or even real estate prices. He noted, however, that central bankers must be concerned when they sense that irrational exuberance is driving a boom that could lead to a bust. When the stock market affects the economy, then central bankers must get involved.
Greenspan's use of the phrase irrational exuberance caused stock markets to decline the next day. That is because investors became afraid that the powerful Federal Reserve Chairman would raise interest rates to slow down the economy. Ever since then, the term irrational exuberance has become a rather famous phrase used to describe stock market booms.
