Basically what's in the title: How did mundus come to mean both world and clean? L&S lists a number of other meanings, but in my knowledge these are two very frequent uses, that do not seem to have much in common.
I have always wondered whether there is any documented history to explain such different meanings. Was it just the fruit of convergent evolution, a complex process of meaning change from a common original meaning, or something different? I find it even funny that with time in Ecclesiastical Latin both meanings came to be close to opposite: the World as the realm of sin and death, and cleanliness as the absense of evil.
My research so far:
There is a Proto-IE root related to mundus meaning to adorn, which would explain most of the clean meaning, but I have not found anything for the world part.
Latin also has the words Terra and Universum.
Terra means Earth (as a part of the whole world, as I understand from the first quote to Cicero in L&S, which makes sense to me). It also has a close PIE root with the same meaning. That seems to suggest terra predates mundus.
About universum I do not have so many clues, except that it seems to be a composite of uni+versus, the later having some ancient semantic field related to turning.