A valuation multiple is a shorthand for a much longer statement. When a share trades at 20 times earnings, the market is saying something about expected growth, the durability of that growth, the risk attached to it, and the rate used to discount it. Compressing all of that into one number is convenient and lossy.
P/E = share price / earnings per share
Sometimes described as the years of current earnings you are paying for. That framing assumes earnings never change, which is precisely what it is trying to tell you about.
Multiples are also only comparable within similar businesses. A software company with 80% gross margins and a supermarket chain with 3% net margins will trade at very different multiples for entirely legitimate reasons. Comparing them tells you about the industries, not about which is better value.
Common belief
"This index is at a historically high P/E, so it must fall."
What is actually true
Multiples have stayed elevated for years at a time, and the level of interest rates changes what multiple is reasonable — a lower discount rate justifies a higher multiple arithmetically. Valuation has been a poor short-horizon timing tool historically, while carrying more information over long horizons.
Two companies trade at 12 times earnings. The first has grown earnings 10% a year for a decade with stable margins. The second has flat earnings, a declining core product and rising debt. The multiple is identical and the two investments have nothing in common.