Normality has to do with the number of equivalents of solute in a litre of solution.
There can be two different definitions of "equivalents" if we are speaking of acid/base chemistry then if is defined as the mass of a substance that donates or accepts one mole of protons. As mentioned before sulfuric acid is diprotic, therefore one half of a mole of H2SO4 donates one mole of protons.
In redox chemistry an equivalent is the mass of a substance that donates or accepts one mole of electrons.
Using Normality to describe the concentration of a solution is very common in my part of the world.
I am sure this has all bee said before,
EDIT[\red]I will also add that in my limited experience many if not all "standard volumetric solutions" i.e. highly pure, solutions used in standardization, and what not, are usually expressed as normal solutions. I can personally say that I have not seen many volumetric standard solutions expressed in Molarity. This is not to say of course that it does not exist but I will speak from my own experience and feel confident that most of the standard solutions offered to myself are expressed in equivalents of solute or Normality. i.e. 12 Normal HCL, dilute 500mL 12N HCL with 500mL H2[/bub]O to yield 6N HCL.
regards,
m_e