At a high level, 'normalization' means making some changes to various data such that their characteristics can be compared in the same space
In this case, normalizing rel per curves usually involves
(a) Changing Sw to normalized water saturation which for oil/water is Swn = (Sw - Swir)/(1-Sor-Swir).
You now have rel perm data defined from Swn = 0 (residual water) to Swn=1.0 (Sw = 1-Sor)
(b) Dividing all the rel perm values by the rel perm to hydrocarbon at residual water, so that (for example, oil/water) at Swn=0, Kro=1. Sometimes this is also done for the water line
Now you have a family of rel perms, all spanning the same ranges, which you can compare/overlay and look for similarities/groupings in shape/curvature. If you do find a family shape characteristic, then you normally fit a corey type exponent to it, then try to fit a set of equations to predict the endpoints as a function of (for example) perm and/or facie. Given these relationships, you can now make a reasonable prediction of any of this family of rock in your reservoir.