The thin lens equation is 1/f = 1/do + 1/di, where
- f = focal length
- di = image distance = distance from lens to sensor
- do = object distance = distance from lens to subject.
The focal length of a lens is defined by the thin lens equation, and it can be interpreted as a measure of the inverse strength of the lens. If you make a lens's optical surfaces more strongly curved, or if you increase its index of refraction, it gets stronger, and the focal length goes down. When you change do and di so as to maintain focus, the focal length f normally stays constant; this is what justifies interpreting it as a fixed property of the lens. (As pointed out in a comment, some lenses do contain moving parts that allow them to automatically change their focal length, but this is a side issue.)
So what's the correct term for “stuff at this distance will be in focus” then?
Generically, in optics, this is called the object distance. In photography it can also be referred to as the focal distance.
everything I've read seems to suggest that focal length is actually a slightly odd way of describing the field of view of the lens
Not really. Focal length just happens to be related to the magnification and field of view.
A possible source of confusion is that in many cases when you're doing photography, do is much greater than di. Under these conditions, di is approximately the same as f. Therefore some people may be under the impression that the focal length is defined as the distance from lens to sensor. But in reality, when you change the focus on your camera, di changes while f stays the same.