I hear people exclaim what sounds like "manager" or "management" when they're agitated. What’s the meaning?
That someone's not happy. Mannaggia is a "polite" vulgarity, an interjection that qualifies as a vivid kind of "dammit." The word has southern roots (it was included in the country's famous Neapolitan-Italian dictionary of 1887) and derives from "male ne abbia," basically "plenty bad." Its literary background stems from another, now outdated interjection, malannaggia, as in "abbia il malanno," or, "May you be damned..." ("Malannaggia l'anima tua!" wrote 19th-century Sicilian author Giovanni Verga, "Damn your soul...")
Mannaggia a me, for example, literally means, "Damn me!" which can cover anything from forgetfulness (there a lot of that around) to rage over missing a plane. Mannaggia a te is what you'll hear people murmur if they're annoyed with you but don't want it to go much further.
The expression can also help defuse a situation when one person's in the wrong and doesn't want to admit it. Better to curse yourself than suffer the imprecations of others.