We are looking for turning points in a trend.
If you draw a trendline on a downward price series, obviously you get a line pointing downhill.
Sometimes, not always, when you have an indicator plotted also (almost any will do), and draw the trendline on the indicator peaks or troughs, you may see the price trendline, and the indicator trendline point in different directions. One downhill, and one uphill. Thats a divergence.
It tends to show that perhaps a price is still falling, but the selling power is not as strong as before, and maybe a change is due.
It works on tops and bottoms. Its a good warning at a double-top when the trend on the price peaks are still uphill, but the indicator peaks point downhill.
I use Dirmov (on AIQ), OBV, and RSI.
Use it as an early indicator, not for exact timing.
Have a look at Corus CS# a couple of months ago. The price was in a long downtrend but the Dirmov trendline started pointing uphill. Couple that with an RSI or Stoch buy signal and we could have got in at ~50p, and walked away with a nice 40% in 2 months.
TFC seems to be showing divergences now.