Something that is inappropriate or unacceptable behavior is unseemly. It's a gentler, somewhat nicer word for "inappropriate" than its synonyms, the "in" words: "indecent, indecorous, indelicate, inelegant, inept" — well, you get the idea.
Knowing that the "un-" prefix turns a word into its opposite, you'll see that unseemly means "not seemly." Let's look at that word (which is related to our verb seem), because it carries the real meaning. Seemly goes back to around 1200, to the Old Norse word soemr, "fitting, becoming." The negative "un-" was added in the early 14th century to denote the opposite meaning. "Seems" to make sense, doesn’t it?