When a Skeptic claims that something (e.g. knowledge, free will) does not exist, a tempting response is to point to the world, and say, "There's some important difference between this case and that one, so I'm just talking about whatever it is that sets the former apart. You can't deny that there is such a thing." For example, there's an important difference between our ordinary actions and those performed out of compulsion -- e.g. hypnotic suggestion or mental illness. It is arguably just this difference that talk of 'free will' is supposed to track. Is this a legitimate anti-skeptical move?
It's always open to the Skeptic to argue that there isn't really any such "important difference" there. We assume there's a difference, but it may be superficial. A skeptic may argue that on closer examination we will find the various cases to be relevantly similar. That's a fine counter-response, if they can manage it. It shows that the anti-skeptical argument from ostension is never a knock down argument. But I think it may often serve an important philosophical purpose nonetheless.
Skeptical arguments often proceed in a very 'top-down' form. They start from a theoretical assumption (e.g. that knowledge requires certainty, or that free will requires ultimate sourcehood), and go on to show that nothing can meet this assumed requirement. That's fine as far as it goes, but if a requirement is impossible to meet, that should set off some alarm bells. In particular, it should make us question whether it's really such an important requirement after all. And that's where the argument from ostension comes in. It's a way to bring the Skeptic's theoretical assumptions into question. Maybe the Skeptic can meet the challenge, but it's often worth asking.
It's easy to make mistakes when one is engaging in a priori theorizing, after all. So the bottom-up (ostensive) method serves to keep us grounded, reminding us of the (apparently) important distinctions that our theorizing sought to capture in the first place. This assumes that intuitions about particular cases are generally more reliable than top-down theoretical intuitions; but that strikes me as a fairly safe assumption. (It is possible for systematic theorizing to override more particular judgments, of course; but some justification is required. Not just any old theoretical intuition will do.)