Average true range is an average of the past 14 candles (price movement graphic), as a default parameter. In order to understand true range, know that it is the same as the high-low range, but also factoring in gaps. This means that true range is the largest of the absolute value of the three: high - low, high - previous close, and previous close - low. Absolute value in this case means that all calculations are translated to positive numbers. 

The meaning of the ATR formula is how the high minus the previous close can be greater than the high minus the low if it gaps from much lower, and the previous close minus the low can be greater if it gaps from much higher.

<ATR image retrieved from thinkorswim>

While ATR is a type of volatility, it is not how options implied volatility was arbitrarily modeled, although it could have been. The way implied volatility ended up being defined is as the 68.3% confidence (one standard deviation) percentage move over a year based on option prices. Similarly, realized volatility is the one standard deviation percentage move for a period of time based on historical prices.

ATR is another way to think about realized volatility (which is not based on standard deviation). ATR is not the same as what we operationally refer to as realized volatility, but it is very similar by analogy. 

In essence, ATR informs us on how wide the active range is. By default, ATR, like other indicators, refers to the daily chart. However, it can be used on any interval, such as the 1-minute or 5-minute candle. On the tactical side, ATR can be used as an effective stop loss substitute (a predefined exit point where there would be a max loss), or as a stop-and-reverse indicator for trend direction. In summary, ATR is a way to see exactly how wide the active range is while also factoring in the gap.