Average True Range (ATR) is a technical analysis indicator developed by J. Welles Wilder, based on trading ranges smoothed by an N-day exponential moving average.
The range of a day’s trading is simply high − low. The true range extends it to yesterday’s closing price if it was outside of today’s range:
true range = max(high,closeprev) − min(low,closeprev)
The average true range is then an N-day exponential moving average of the true range values. Wilder recommended a 14-period smoothing. Note this is by his reckoning of EMA periods (see the EMA article on that), meaning an α=1/14.
The idea of ranges is that they show the commitment or enthusiasm of traders. Large or increasing ranges suggest traders prepared to continue to bid up or sell down a stock through the course of the day. Decreasing range suggests waning interest.