Median Absolute Deviation (MAD) is a measure of variability in a sample of data, and is often used as an alternative to measures like standard deviation since it is more resistant to outliers. Use the [mae] tag if you are asking about the point forecast accuracy measure called MAD or MAE.
The MAD (Median Absolute Deviation from the median) of a sample $X_1, X_2, ..., X_n$ is
$$ {\rm MAD} = {\rm median}_{i} (|X_i - M|) $$
where
$$ M = {\rm median}( \{X_1, X_2, ..., X_n \} ) $$
It is used as a measure of dispersion in a data set for being a robust alternative to measures like the observed standard deviation, since it is less sensitive to outliers. It is not to be confused with the mean absolute deviation, $\mathbb E^X\{|X-\mathbb E^X[X]]\}$ or its empirical version.
