Soap is made up of two parts, a hydrophilic part and a lipophilic part. The hydrophilic part loooooves water while the lipophilic part is much more partial to lipids (that is, fats and oils). When the lipophilic part comes into contact with an oil or fat, it hooks on to it. When the hydrophilic part comes into contact with water, it hooks on to that. So now, we've got a molecule of soap connecting water and oil together very strongly. This molecule pulls the dirt away and dissolves into the water, getting rinsed away.

The outer layer of bacteria -- their cellular membrane -- is made primarily out of lipids. So the lipophilic part of soap will attach itself to bacteria and cause them to get pulled along with water or interfere with their connection to your skin. Bacteria are pretty big when we're talking about the molecular scale of soap action though, so while this will remove some bacteria, if bacteria make an effort to stay attached to the skin, they will probably succeed.

So what can we do to deal with that bacteria? Let's change up the formula some and try a different sort of chemistry. Rather than just using soap to attach to the cell membrane and drag the whole thing away, how about we destroy the cell membrane and kill the bacterium outright? Different chemicals work in different ways to achieve this aim. Some chemicals, like benzalkonium chloride will react with the lipid layer of a cell membrane directly destroying it or causing the bacterium's insides to leak out of its pores as they lose cohesiveness.

Now, that's gonna be rough on our skin, so a more targeted approach is in order. We can interfere with the production and replenishment of a bacterium's cell membrane. Chemicals like triclosan do this very well, binding to enzymes in bacteria that help them to make their cell membranes, but that aren't found in humans and as such aren't dangerous to us. Because the bacteria can't maintain their outer membrane, eventually they lose their skin and become the microbial equivalent of skeletons with all their organs. That might be some kind of zombie. I don't actually know any ghost stories that single-cell organisms tell. I'm not really good with human ghost stories either, come to think of it.

But that's how we get clean: we dissolve and rinse away dirt, we destroy the fatty cell membranes of bacteria or we interfere with the biological processes of bacteria. There are probably a number of other biocidal mechanisms that can be used to kill bacteria and are suitable for use in soap, but those two are very common, found in household cleaners and bathroom soaps.