In the chart below of the S&P 500 exchange traded fund (SPY), Momentum divergences can be seen:
The first bearish divergence occured when price formed a double top formation. The Momentum indicator confirmed when price of the S&P 500 ETF failed to make a higher high.
The next divergence was a bullish divergence, where price made lower lows, yet the momentum indicator made higher lows. This signaled that the recent downtrend was losing steam and that a bottom could be forming.
The last divergence occured because the S&P 500 ETF was increasing, but at a decreasing rate. The momentum indicator shows this perfectly, by making lower highs over the course of about 15 stock trading days.
Just because a stock trader or futures trader sees a divergence doesn't mean that they should reverse their stock or futures trade. Divergences warn of potential reversals. A more concrete signal, like a trendline break would have been a great signal in the last example. Nevertheless, the Momentum indicator offered the stock trader plenty of time to reduce the size of their long stock position.
The Momentum indicator is a simple yet effective technical analysis tool, offering suggestions as to when to buy and sell and warning of potential price reversals. A similar, and arguably superior tool for measuring momentum is the Rate of Change indicator.