In my understanding, "the absolute correlation" is not such a common expression. Can anyone kindly explain the significance of the built-in symbol AbsoluteCorrelation, especially compared with Pearson's and Spearman's correlation coefficients?

I'd say it's not only "not such a common expression" but at best a very misleading expression. What one obtains is not a correlation measure in the sense that the values are only between 0 and 1.

As an example:

d = MultinormalDistribution[{3, 2, 1}, {{2, -2/3, -1/3}, {-2/3, 3, -1/3}, {-1/3, -1/3, 7}}];
AbsoluteCorrelation[d] // MatrixForm


So one is not getting correlations. I would steer clear of it for any statistical applications at least until the documentation gets better (or even never).

d = MultinormalDistribution[{0, 0, 0}, {{1, -2/3, -1/3}, {-2/3, 1, -1/3}, {-1/3, -1/3, 1}}];