Cleaning

We use soap to clean things when water alone won't remove whatever is on the object.

For instance, If your hands were muddy, water alone would probably be enough to get them pretty clean. Add a brush to get under your nails and you're good to go.

If someone poured oil on your hands you might still not need soap to clean them, a good wipe with a paper towel might get the worst off.

On the other hand, if your hands are greasy (you've been rebuilding a car or eating cookie dough) then water alone won't do the job, because water and grease have very weak attractions for each other.

Wiping with a paper towel won't do it, because the molecules of the grease have been worked down into your skin. Specifically, the long non-polar chains of the grease molecules have been lodged between and around the dried, dead cells on the outside of your skin and wiping with a paper towel won't be able to pull them free.

Sandpaper might do the job by scraping off that outer layer of dead cells, but it would probably hurt a good deal.

So...we use soap.