When an acid is mixed with water it emits hydrogen ions (protons). For example sulfuric acid has 2 hdrogen atoms and so it can emit 1 or 2 protons
Whether it emits one or two depends on the pH of he solution. At any pH > 1.99, which would always be the case in brewing, it emits both. Because of this sulfuric acid is termed a strong acid. Strong here is tied to the number 1.9. Obviously in many cases we want to know the concentration of the hydrogen ions so that we would know, for example, in the context of alkalinity determination, how much alkalinity a given amount of sulfuric acid is neutralizing. The concentration of hydrogen ions is expressed in moles per liter. A mole is Avogadro's Number (6.022 x 1023) hydrogen ions and a mole of hydrogen ions weighs 1 gram. A solution of acid that contains 1 mole of hydrogen ions (1 gram) per liter is called a Normal solution and it's bottle would be labeled N H2SO4. The 1 gram derives from the fact that Avogadro's number of protons weighs 1 gram. The mole of hydrogen ions in N H2SO4 comes from half a mole of sulfuric acid. As the molecular weight of sulfuric acid is 98.079 grams/mol this means that a solution made by adding 49.0395 grams of the acid to 3/4 of a liter of water and then making up to one liter (never water to acid!) would yield a N solution.
If one liter of the solution contains 0.05 mol then the solution is 1/10th normal and is labeled 0.1 N H2SO4.
It is the responsibility of the user to understand that 0.1 N H2SO4 is only 0.1N if the pH is at least 2 units greater than 1.99. This is the case when 0.1 N H2SO4 is used to titrate a water sample to pH 4.3. At pH 1.99, however, half the acid molecules will emit both protons and the other half only 1 for an average of 1.5 so that one half mole of the acid in a liter of water would result in an 0.75 N solution.