Q:

What does 'laterally aligned' mean in this description?

In the Airplane Flying Handbook there is a section on crosswind takeoffs that mostly makes sense. However, this paragraph confuses me.

Takeoff Roll
As the forward speed of the airplane increases, the pilot should only
  apply enough aileron pressure to keep the airplane laterally aligned
  with the runway centerline. The rudders keep the airplane pointed
  parallel with the runway centerline, while the ailerons keep the
  airplane laterally aligned with the centerline.

Laterally is an adverb meaning 'Relating to the direction to the side.'
Later on they use this image which shows the lateral axis.

When I take off in a crosswind in an airplane with nose-wheel steering the rudder pedals are used to keep the plane on the centerline. The ailerons are deflected into the wind to keep the windward wing from rising. 
So what do they mean when they say that “the pilot should only apply enough aileron pressure to keep the airplane laterally aligned with the runway centerline”?
Edit: I don’t think they are referring to keeping the wings level as some commenters say. This image from the same section somewhat exaggerates the effect but ailerons are used to keep the upwind wing down.

A:

The only meaning that I can conceive of is that "laterally aligned with the centerline" is a fancy way of saying "on the centerline"—or, at least, keeping the distance from the centerline under control, so that you don't drift off of the runway.
The paragraph seems to be describing the following technique for lateral control during a crosswind takeoff:

Use the rudder to keep the heading (the direction the nose is pointing) parallel to the runway centerline.
Use the ailerons to control the bank angle so that the airplane stays approximately over the runway centerline.

The reason the Airplane Flying Handbook uses the word "laterally" here is that the ailerons are being used to control the airplane's lateral (left-to-right) motion.
Some comments speculate that the paragraph is really saying that the ailerons should be used to keep the wings level. That doesn't make sense to me; in a crosswind, if you're using rudder to keep the nose parallel to the centerline, and you're keeping the wings level, then you'll drift downwind off the runway.

