[svara]

It's explained in more detail further down in that paragraph, I think the wording is fine.

The axis argument gives the index of the axis along which your summate, and which therefore disappears after summation.

There might be a confusion about whether "axis 0" is rows or columns? Its length is the number of rows, but it "points" along columns.

I prefer just calling them axis 0, 1, 2, ... and avoid thinking about rows and columns in numpy, I've found that sometimes avoids confusion.