That is, it's twice the radius where the radius is from the centre of the sun to some edge. But what is that edge?
Fusion reactions taking place inside the core of the star produce a huge amount of energy, most of which becomes heat. These reactions are not evenly distributed through the star and so there are phenomena such as sun spots and solar flares, however the total amount of energy produced tends to be reasonably constant.
I would say that the edge is defined by the average point where the gravity reaches equilibrium with the pressure of the star's super-heated gases (as a result of internal fusion).
See the picture of the Sun on Wikipedia
That edge/balance will change when the sun begins to run low on hydrogen. At this time, the reactions inside the star will change causing it to become become a giant red star.
I guess you could compare it with the surface of sea water on Earth. It's technically not still and stable, but we can calculate an average value of the sea level. And it is because it's an average value that we can rely on that to determine altitude and earth radius as well.
Look at the Sun. You shouldn't do this directly with the naked eye, but you can do so through a very dark filter, or project a suitably dark image through a pinhole. You can even find photos of the Sun on the internet.
What you see is a disk, uniformly bright and with a sharp boundary, surrounded by a comparatively must darker sky. The bright region is the part we consider the Sun, and that's how we get the radius.