Divergence is a discrepancy between the movement of the indicator and the chart. Divergence usually indicates a trend reversal.
So, if the chart lines form a series of maximums, but the Stochastic lines, in contrast, are descending, you can expect a descending trend to start.
If the chart traces a series of new minimums, but the Stochastic lines have started rising, you can expect the price to start to rise.