The word skyfall is not normally used, except as the title of various works of fiction; it is not a regular noun. However, the general idea that we would all be in severe trouble if the sky should fall down is widespread and immediately recognised throughout the Western world, including Anglo-Saxon countries.
What exactly is Skyfall?
The story centres on Bond investigating an attack on MI6 that leads to a wider plot by former agent Raoul Silva to discredit and kill M as revenge for abandoning him. It sees the return of two recurring characters after an absence of two films: Q, played by Ben Whishaw, and Miss Moneypenny, played by Naomie Harris.
Why did the psychologist say Skyfall?
Skyfall wasn't just his old home; his parents also died there, and he hadn't been there since their death. So, when the psychiatrist says 'Skyfall', he actually wanted to check if he had moved on from their death or not. 'Done', was probably Bond's way of saying 'Yes'.