The quality of abruptness is an almost rude bluntness or suddenness. When you act with abruptness, you do something quickly, with no warning or consideration of how other people feel about it.
Friends will comment on your abruptness if you suddenly walk away from them in the middle of a conversation. If your favorite restaurant is unexpectedly shut down one day, with a sign saying "out of business," you'll wonder at the abruptness of its closing. The word at the heart of abruptness is the adjective abrupt — and it is rooted in the Latin word abruptus, which means "broken off or disconnected."