Soap is a substance used to help clean a persons body from rubbing it on them while bathing and rinsed off with water afterwards. It commonly comes in the form of a solid bar or can come in liquid form in a bottle. Sometimes when it is in bar form, a character may comically slip on it if left on the ground. Shampoo is a form of soap that is specifically for hair.
After Megu Kanzaki's Clawfoot Bathtub was rigged to drive through town while she was still having a Bubble Bath in it, she is then seen pulling out a bar of soap and start washing her arm in a panic. As the tub hits a small bumb, Megu drops the soap and where it gets left behind as she remains in the tub as it continues to drive off.
The episode's title card is a parody of the cover to the movie fight club with a giant bar of soap in the center. The soap bar seems to be creating Bubble Bath which Panty and Stocking are shown to be bathing in.