The relevant text on Page 13 of Fate Core is, "Sometimes, you want to add a detail that works to your character's advantage. [...] To do this, you'll spend a Fate point."
I think of it as similar to other spending-a-Fate-point scenarios. It's done in order to instantly affect the course of the fiction, in a way which directly benefits the outcome to the player of a plot point which is immediately (as in, right now) in play and being decided/resolved.
There is one small difference: Keep in mind, too, that whatever the Story Detail is, it remains true forever (unless gameplay changes it). In the Fate Core example, Zird will still be able to communicate with speakers of this particular village's language even if the scene, session or adventure ends and he encounters such people again in a totally different scenario. This can be considered, when deciding whether or not to ask a player how bad they want it.