Looking at sci-kit learn regression metrics, it gives us 5 metrics: explained variance score and $R^2$ score; mean absolute error, mean squared error and median absolute error.
The explained variance score and $R^2$ score are related and well explained on Wikipedia.
The same occurs for mean absolute error and mean squared error, two metrics commonly used (and well explained on this topic: while the mean absolute error considers all the data, but doesn't "weight" outliers, the mean squared error helps us to check for outliers.
But what does the median absolute error says about the data and the response of the models?