When. Anywhere and constantly — it is the most frequently reported supplication of the Prophet, and it is said at the end of prayers, in tawaf, and by people who want one sentence they can rely on. Many make it the closing line of every other supplication.
The words. Hasanah is left indefinite, and that is the whole design. It is not 'wealth' or 'health' or 'a house'; it is 'a good thing', unspecified. The one asking does not have to know what is good for him, and cannot mistakenly ask for something that would harm him. The word is repeated for the two realms — the same request, made twice, once for a world you can see and once for one you cannot. Then qina, from wiqayah: a shield, a covering placed between a person and a thing. Not 'save us from the Fire' after the fact, but 'put something between us and it'.
Why the third clause is not redundant. Good in the Hereafter would seem to include safety from the Fire. Naming it separately makes the fear explicit rather than folded into a general hope, and it is the clause people say with the most attention.
Where it is from. The Qur'an, al-Baqara (2:201), where it is given as the speech of those who ask for both realms, set immediately against those who ask only for this one.
On its brevity. It is short because it is meant to be carried. A person who knows only this one is not poorly equipped; it covers everything a longer list would try to enumerate.