The W value is essentially a count of the number of sub-hypotheses that have passed for a given species.

Underneath the hood, ANCOM is just running bunch of pairwise tests. Each sub-hypothesis is structured something like follows (for the 2 class case)

H_{0 (ij)}: mean(\log \frac{x_i}{x_j}) = mean(\log \frac{y_i}{y_j})

where x_i denotes the ith species abundances from samples x, x_j denotes the jth species abundances from samples x

and where y_i denotes the ith species abundances from samples y, y_j denotes the jth species abundances from samples y.

The W value is just a count of the number of times H_{0(ij)} is rejected for the ith species.

So if you have 1000 species, and W=60, for OTU k, then H_{0k.} is rejected 60 times. This basically means, that the ratio OTU k and 60 other species were detected to be significantly different across the x and y groups.