I agree that was a good description.
A picture that might be useful:
[from kayarchy site]
The bottom piece of wood has obvious runout. A piece of wood like this, with a rectangular or square cross-section, can have grain runout on any of its four sides (depending on which way the piece of wood is placed/set down. Likewise, if an axe handle had a similar rectangular cross-section, the grain runout (if it exists) could be found on any of the four sides of the handle, depending on how the piece of wood is arranged before the handle is machined.
The actual shape of an axe handle makes this more complicated, with some rounded sides and some sections that swell or bend. Where there is a swell (or, conversely, a necking down) in the handle, there will be some "runout" here, even in a straight-grained piece of wood, so this is generally not a problem.
When looking down an axe handle from knob end toward the head, if the grain is "perfectly aligned" at the knob end, then the runout would tend to show up on the cheek sides of the handle (not the bit or poll sides). The curve at the head end of the handle typically shows some runout, unless the piece of wood naturally has a curved grain here (homemade handles can take advantage of such grain) or unless the grain remains "perfectly aligned" along the whole length of the handle.
The handle is thicker at the head end, so some runout here is not as problematic as it can be at the thinner sections along the length of the handle.
These are my impressions, anyway. Maybe somebody with a better understanding will add some clarifications.