Here is one of the definitions from the OED, I hope it helps you see what they're referring to:

meridional

4 Of a marking or structure on a roundish body: lying in a plane with the axis of the body.

May be this use of “meridional” (=of, pertaining or related to a meridian) is related to the following meaning of “meridian”:

"Meridian
A line of constant longitude on a spheroid (or sphere). More generally, a meridian of a surface of revolution is the intersection of the surface with a plane containing the axis of revolution."
<http://mathworld.wolfram.com/Meridian.html>
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Best luck,
Manuel

One thing is sure: For you to vizualize the flow [of fluids and air] through a general rotor, you have to draw a meridional surface and depict the blade threon for calculations.

Meridional in your text has to do with the chord, which is the length of the perpendicular projection of a blade profile onto the chord line.

My suggestion is for you to refresh your knowledge on geometry [particularly, the lines passing on a circumference, and check what a chord line is, but as applicable to thermodynamics]

As this is a complex matter, involving thermodynamics, I reinforce Bill's suggestion for you to check his site, as above recommended.

Once again, meridional, in this case, refers to all possible vertical lines [opposed to horizontal] possible to be drawn on a circumference, or any curve surface. However, you should stick to the meridional phrasing, as this is standard to the discipline at hand.