Something that was much insisted on when I was at school, because i guess some kids found it hard to get their heads round. Like 1M HCl or NaOH are 1N but 1M H2SO4 or Na2CO3 are 2N. You get the idea? - it's the same as the distinction between molar masses and equivalent masses (or weights as we used to call them).
I think they have been phased out of teaching now, have they? If so it's no loss, they are unnecessary.
Normality meant different things at different moments in time. There was a period when normality depended on the reaction - so 1M sulfuric acid was 2N in the reaction with NaOH, but 1N inteh reaction with CaCl. Then IUPAC decided to make it always reaction with H+ or e- - so 1M sulfuric acid would be always 2N. Then, IUPAC decided they created so much confusion it is better to deprecate normality at all.