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