The Deviance is a special quantity that is a generalization of the residuals in normal linear regression. The unit deviance can be thought of a distance, or a discrepancy, between the observation and it's mean. Under mild assumptions the scaled version of it distributes chi-square with 1 degree of freedom. The total deviance, is the sum of the unit deviances. The scaled version of it distributes chi-square with n degrees of freedom. The null and residual deviances, are the total deviance after the model is fit using maximum likelihood. The null corresponds to a simplified model with only an intercept, where as the residual corresponds to the full (currently tested) model. The residual deviance = RSS for the normal distribution. This gives us a way to assess the overall goodness of fit of the model, as well as the specific coefficient necessity in the model.

Correction, at 02:19 (and subsequently) - should be "when mu is equal to y" we are maximizing the mu here.

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Recommended book: Generalized Linear Models With Examples in R; Authors: Dunn, Peter; Smyth, Gordon; https://www.springer.com/gp/book/9781...