An indicator divergence is simply when price is moving in a direction opposite of an indicator. I personally like using oscillating momentum indicators for monitoring divergences and have included a stochastic in my methodology for doing so. In general, oscillating indicators follow price swings up and down which creates their own swings. The direction of price and the indicator are best seen with lines drawn between two swing highs or two swing lows.
Divergences are determined by comparing the slope of the line between the price swings with the slope of the line between the indicator swings. If the slope of the price swings is up and the slope of the indicator swings are down at the same time, then price and the indicator are diverging. Likewise, if the slope of the price swings is down and the slope of the indicator swings is up, the price and the indicator are diverging.
Why are divergences worth monitoring?