Imagine a drunkard leaving a lamp post, each step equally likely to go left or right. Where will they be after a thousand steps? Not where they started. The distance from the lamp post grows, though in no predictable direction. This is a random walk, and it describes stock prices, the diffusion of molecules, the path of a pollen grain in water.
The surprising thing is the square-root law: after n steps of size 1, the typical (root-mean-square) distance from the start is √n, not n. Quadrupling your time only doubles your uncertainty. A four-year forecast is twice as uncertain as a one-year forecast, not four times as uncertain.
Random walks also explain why past prices carry almost no information about future prices in efficient markets. Each step erases the memory of the last. The path looks meaningful in hindsight. It was not.
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