Self-aware describes someone who understands their own character — how they act, what they are good and bad at, and how they come across to other people. The key part is that last bit: a self-aware person can see themselves a little from the outside. So if a man says 'I know I talk too much, sorry, stop me any time', that is self-awareness. It is an adjective, used before a noun ('a self-aware writer') or after be/seem ('she's very self-aware'). It is a modern word, common now in psychology, in job interviews, in talk about mental health and about comedy. In the last twenty years or so English has stretched it to things that are not people: a film, a book, a TV show, or a joke can be self-aware, meaning it knows exactly what kind of thing it is and lets you see that it knows. 'The show is funny and pleasantly self-aware.' It is almost always positive; the opposite, 'not very self-aware', is a gentle but real criticism. Note the difference from 'aware' alone — 'aware' means you notice what is going on around you, while self-aware means you notice what is going on in you.