the presentable dignity a private part is given by being covered: seemliness, modest decorum
This word appears only once in the New Testament, in Paul's picture of the church as a single body with many parts (1 Corinthians 12:23). He says the parts we treat as "less honorable" are the very ones we dress with the greater honor, and "our unpresentable parts" are given the greater seemliness. Nearly all scholars read this as tactful language for the private parts of the body: the honor they receive is precisely the dignity of being clothed and kept from view. The word names that conferred presentableness, not a modest attitude in the person.
Paul is building a play on words that English cannot copy. He pairs this noun with its opposite in the same breath: the "unpresentable" parts (ἀσχήμων) are the ones given extra "presentableness." The whole family of related words stretches between two ideas: on one end, graceful, fitting, decent appearance; on the other, the social standing of a well-regarded, prominent person. The adjective in this family (εὐσχήμων) can mean either "presentable" or "of high rank," and the adverb (εὐσχημόνως) means acting "decently" and in good order.
That double range is the point of the passage. Paul talks about the honor and shame of body parts while thinking about the honor and shame of people in the church. Just as the body gives its greatest care to the parts it hides, so God gives the greater honor to the members the community counts as weaker or less impressive, so that there would be no division in the body.