I am pretty sure that you are looking at "Average Roughness Height". Not sure what the second "a" stands for. The measurement is always in microinches. You are looking at 250 X 10 -6 inches, and so forth. The measurement is from the peak to valley of the bumps making up the surface roughness.

250 microinches can be acheived with power saws. 125 can be acheived with milling, and 63 can be done with laser cutting. Less than 63 requires grinding or honing.

Smoother is always better but there is a tradeoff in cost, of course.

aarh?
I wasn't certain, so I looked at my copy of ASME B46.1-1985, SURFACE TEXTURE. The closest I see to this is the description of Roughness Average Ra, AA or CLA, depending on what country, "Arithmetic Average Roughness".
Since we're doing this for Acedemia's sake,
the approximation formula is   Ra=y1+y2+y3...+yN / N
Where
Ra = arithmetic average deviation from the center line (of the surface)
y = ordinate of the curve of the profile ( absolute value )
N = number of increments

Eric Johnson

I understand that the selected flange surface finish depends on gasket selection.

For nonmetallic gasket sheet, it can be compressed to the flange serration. This type of gasket is suitable for FF (flat face) flange which is 250-500 AARH.

For spiral wound gasket, it always use with RF (raised face) flange which is 125-250 AARH.

For metallic gasket and metal jacketed gasket, very smooth flange surface (63 AARH) is suitable for this application.

what does rms stand for as it pertains to flange faces.

RMS means Root mean square value of the roughness.

Arithmetic Average Roughness Height (AARH)

If you are machining new gasket surfaces, not a problem.  If you are cleaning up the face of an existing pressure boundary ANSI flange, measure the flange width first and compare to minimum ANSI tolerances.  You might need a new flange.