Expressing different chemicals as one common chemical material makes it easy to add their concentrations to get their total effect. As an analogy, consider a wealthy person with bank accounts in several countries. In order to calculate his total wealth, you must express each currency in terms of a common unit (such as ounces of gold).
For instance, constituents that are often quantified as CaCO3 (calcium carbonate) are "hardness" species (divalent metal cations such as Ca 2+ and Mg 2+) and alkalinity species (hydroxide OH -), carbonate (CO3 2-), and bicarbonate (HCO3 -).
Expressing these species in terms of a single component (the common unit, in this case calcium carbonate) allows the individual species to be summed, indicating their eqivalant total reacting capacity.
Nitrate, nitrite and ammonia are often expressed as nitrogen - N
Sulfate, sulfite and other sulfurous compounds are often expressed as sulfur - S