Jonny was about to sit down when his father came into the house.
What does this "about" mean?
What usage is this?
In this context “about” means at that very instant, at the precise moment when his father came into the house.
edit: My answer doesn't apply to the above after Tyler edited it, so to avoid confusion, here is what the quote said originally:
Johnny was about sitting down when his father came into the house
This is my answer: /edit
It's an informal, and fairly colloquial to the American South, way of saying "Johnny was about to sit down" or "Johnny was just about (i. e. nearly) sitting down" when his father came into the house.
On the other hand, if a British or Australian person were to say it, it would mean that he was sitting down around the house when his father came in. (Punctuating this "Johnny was about, sitting down, when his father came in" makes this meaning more clear.) More typically in this case they would say "Johnny was sitting about when his father came into the house." Americans would say "sitting around" with the same meaning. Americans walk around, sit around, drive around, and so on. Brits walk about, sit about, and drive about.
Two Brits having a "kickabout" are kicking a soccer ball back and forth to one another; a rough (well, very rough) American equivalent is "playing catch." Perhaps with the growing popularity of soccer in our country kids will start having "kickarounds", and maybe already do.
It means that Johnny intended to sit down, and his father came home the moment before he would have begun sitting.