Eli5
Imagine a soap molecule is a long chain with two special velcro hooks on each end.
One end of the chain likes to hook to water, the other end of the chain likes to hook to oils.
When you cover your hands in soap, you’re moving these chains around your hands, and they find all the oils and nasty stuff and hook onto it.
When you run the water, the water hooks onto the other end of the chain and carries the soap away, taking the nasty stuff with it.
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