The ADX is part of the direction movement system introduced by J.Welles Wilder in his book New Concepts in Technical Trading Systems. It comprises of the Directional Movement lines _ the plus DMI line and the minus DMI line _ and the ADX line (the Average Directional Movement Index)

ADX is created with reference to both positive and negative directional movement and identifying sustained movement in one direction. When this occurs ADX will rise (irrespective of whether the trend is higher or lower). Trend direction is identified by whether positive movement (DMI+) is above or below negative movement (DMI-). Once ADX rises above a certain level a trend can be said to have been established.
Although the average directional movement index (ADX) isn't used as frequently as some of the popular technical indicators the ADX line has definite advantages because it filters out a lot of the false oscillator signals which are frequently given early in a move.
A trader can stay with trending positions longer by following the simple guidelines for the ADX line. A climb by the ADX line above 40 followed by a downturn, signals an imminent end to the current trend (whether up or down).

The ADX is less helpful during sideways markets. During extended consolidation periods the ADX line will slip toward 10. When ADX approaches 10, a major move is usually about to take place. But the ADX line doesn't tell you which direction it will go. You have to rely on other indicators for the probable direction of the next move.
In short, if the market is trending, the ADX line should be rising. During an extended consolidation period the ADX line will slip toward a low number.

To sum it up _

When the ADX starts rising from a low level it signals the beginning of a trend.
The trend is confirmed when the ADX ha s risen above the 20-25 value and the +DMI line has crossed the _DMI line (in case of an uptrend)
 
When the ADX has reached an overbought level of 40-50 and starts consolidating or turning down it can signals the end of the current trend.

The decline of the ADX signals the consolidation or indecision of the market.
The optimum use of this indicator would be to consider trades only when the ADX has started to rise from a low level, as it indicates that a sideways basing pattern has been formed and trends usually emerge from extended sideways periods giving highly profitable trades.

The chart example shows how the ADX effectively indicates a range bound area and the breakout forming the subsequent trend.