I think the equation was just rearranged so that you can see where the poles and zeroes are. But the equation does look a little odd to me with the "wz/s" term in the numerator. That just doesn't look right...
It is called an "inverted zero". It is just a simpler way to write the transfer function. The inverted zero is formed by a pole at the origin + a real zero.
To get familiar with transfer functions in depth, there are books. Microelectronics books generally have a chapter in transfer functions e.g. Sedra and Smith.