Elision of “I am important,” - used to describe someone who implicitly or explicitly believes that he or she is important, and is likely to be thinking “I am important” at any given moment.
Observer #1 - “My goodness but Edwin is full of himself today!”
Observer #2 - “Indeed he is - he’s a very amportant person.”
Acting important when you are in an airport, by wearing clothing that conveys authority or worldliness, striding purposefully with a carryon trailing you on wheels, drinking at a bar while apparently doing something critical on your phone.