The Donchian Channel was developed by Richard Donchian and it could be compared to the Bollinger Bands. When it comes to volatility analysis, the Donchian Channel Width was created in the same way as the Bollinger Bandwidth technical indicator was.
As was mentioned above the Donchian Channel Width is used in technical analysis to measure volatility. Volatility is one of the most important parameters in technical analysis. A price trend is not just about a price change. It is also about volume traded during this price change and volatility of a this price change. When a technical analyst focuses his/her attention solely on price analysis by ignoring volume and volatility, he/she only sees a part of a complete picture only. This could lead to a situation when a trader may miss something and lose money. Lets take a look at a simple example how volatility may help a trader:
Most of the price based technical indicators are lagging indicators. When price moves on low volatility, it takes time for a price trend to change its direction and it could be ok to have some lag in an indicator. When price moves on high volatility, a price trend changes its direction faster and stronger. An indicator's lag acceptable under low volatility could be financially suicidal now - Buy/Sell signals could be generated when it is already too late.
Another use of volatility - very popular one - it is to adapt a stop loss strategy to it: Smaller stop-loss recommended in low volatility periods. If it is not done, a stop-loss could be generated when it is too late. Bigger stop-loss recommended in high volatility periods. If it is not done, a stop-loss could be triggered too often and you may miss good trades.