Example 1: Trailing behind the higher lows
A trader is long a market that begins to trend, making a sequence of higher highs and higher lows. Rather than exiting at a fixed target, they trail the stop just below each new higher low as it forms. The trend pulls back several times, but each pullback holds above the prior low, so the stop is never hit and the trader stays in. When the trend finally breaks and price takes out the most recent higher low, the trailing stop closes the trade, having captured most of a move whose end the trader never had to predict.
