How does soap kill bacteria?
Antibacterial soap has an added antibacterial agent called Triclosan. Triclosan works by binding to an enzyme in bacteria called enoyl-acyl carrier protein reductase enzyme (wow, that's a mouth full) or ENR for short. When Tricolsan binds to the ENR enzyme it increases ENR's affinity for a molecule called
Normal (non-antibacterial) soap as I said above do not kill bacteria. Soaps are primarily comprised of fatty acids; when these fatty acids come into contact with water they form what is called a micelle. A micelle is an aggregate of fatty acids (it looks like a bubble) with the hydrophobic fatty acid tails facing each other on the interior of the micelle and the hydrophillic phosphate heads facing the water. The fatty acid tails surround and form a chemical bond with bacteria, dirt, and oil, while the phosphate heads from a bond with the surrounding water. When you go to rub your hands together when you wash them the micelles become dislodged and along with the trapped bacteria, dirt, and oil are sent down the drain. I added a picture below so that we can better conceptualize what a micelle looks like:
Image Courtesy of: SuperManu (Wikipedia user); Accessed at: https://en.wikipedia.org/wiki/Micelle#Solvation; Resued under: CC BY-SA 3.0
In the image above the green ovals, the hydrophillic heads, are attracted to water and the yellow lines, the hydrophobic tails, are attracted to either each other, dirt, oil, or bacteria.
I hope this helps!