Yeah, ya know, I could have avoided the word "rotations" altogether and just stuck to "days" in this title of this thread... you have a point there.
The first thing that helped me wrap my head around this went something like this...
For so-called tidal lock (which thank god we don't have), there would be one long, infinite day, and the notion of "year" is undefined unless you somehow introduce more reference vectors (i.e. directions to stars, cosmic rays).
Next I imagine a different case with one day taking one year to complete. To do this, I keep the earth fixed, i.e. no rotation at all, and then translate it in an orbit around the sun. This will give the apparent view of a sunrise, sunset, etc.
So the trick *just* happened if anyone missed it. We have a case of an earth that does *not* rotate, but it experiences a single day *anyway*.
Now build from there. Suppose we "tune in" exactly one rotation of the planet as we drag it around the sun. Fine, like before, I translate it around a rough circle while twisting it once. As viewed from earth, there are now *two* days, but we only forced *one* rotation.
This off-by-one error goes all the way up to 365 +/- 1. The sign is determined by whether or not the rotation and revolution axes are in agreement.