Matrices are considered to belong to the same equivalent class if they can be transformed into each other by successive permutations of rows or columns.
In general, to transform 2 equivalent matrices into each other, it is necessary to first permute rows, then columns, then rows and so on.
From Brendan McKay, Aug 27 2010: (Start)
A079815 appears on the surface to describe the same objects as A000512, but I don't know where the term "71" comes from.
Also the comment "In general, to transform 2 equivalent matrices into each other, it is necessary to first permute rows, then columns, then rows and so on." is wrong  actually only one permutation of rows and one permutation of columns is enough.
I will guess that this sequence counts matrices in which both the rows and columns are in sorted order. The reason I suspect that is because a common way to make such matrices is to alternately sort the rows and columns until it stabilizes.
The value of a(8) should be checked. (End)
