This a great therad - I never really understood the term "normality" but I was never too bothered about it as it is generally not used any more, in my experience (this is probably not something i should be admitting!).
But to the OP - It seems the normality of a 1 molar solution of an acid which has 2 acidic protons is 2N. it's molarity is obviously 1M.
They are both ways of considering the concentration of a solution, but the molarity relates to the number of molecules of the substance in a solution of a given volume, whereas the normality relates to the number of reactive sites in a solution of a given volume.