The Average True Range was developed by Welles Wilder in his book New Concepts in Technical Trade Systems as a way to measure volatility. For each print, the true range is calculated by taking the greatest value of the 3 following computations:
This true range calculation takes into account the fact that the price may have gapped up or down and never closed that gap, thereby including the gapped price action as well as the current bar's price action to get a true sense of the movement during the current period.
The calculations above are to compute the true range for each candle. The Average True Range creates a moving average of the true range calculations - a 14 candle period is typical.