Once fats are saponified by lye, the properties of the fat (oils and butter) itself change. But lye has a maximum amount of fat it can saponify. Superfatting is adding more fat than the lye can saponify, so that within the soap there is also some fat hanging out.
Some fats, like coconut oil, are very cleansing when saponified. While yeah, you want your soap to clean you, a very cleansing soap can leave your skin feeling dry and tight because the oils on your skin have been stripped off. Superfatting helps offset this tight and dry feeling, to an extent.
Some schools of thought are that the oils provide some benefit to the skin, much like the butters and oils in lotions. I'm not sure how much I follow that, as soap is a product that washes off.