What s the purpose of desaturating an image on Photoshop?

For me, it's a judgment call. I will sometimes desaturate portraits a bit in order to improve a mottled complexion.

If you must spend more than 5 minutes improving an image in post-processing software, then you may as well just throw it away. The exception would be if you happened upon a rare visit by extraterrestrials and you got a quick shot before they bundled back into their spaceship and zoomed off. Technical imperfections would be tolerated.

Depending on the effect you may want, it's all done using layers, layer masks and/or layer modes. Often you will need to duplicate a layer, then desaturate to get the luminance data which is black, white and shades of grey. This can be used as a layer mask now with white being opaque, black being transparent and all the shades of grey allowing opacity based on how light or dark it is. A bit technical but that just scratches the surface. Search on Youtube for tutorials about layers, layer masks and layer modes. Hope this helps.