The phrase "to soak the diapers" means to put the dirty diapers in water or a cleaning solution for a while to make them clean and fresh again. Full definition
Also, you are not soaking diapers in a bacteria filled pail or toilet. (tinytush.com)
By soaking the diapers for about twenty - four hours before washing, stains are easier to remove. (diaperjunction.com)
You might hear the older generation talking about a diaper pail that was used to soak the diapers until they were ready to be washed. (mommyedition.com)