Alkalinity is a measure of a solution's ability to neutralize an acid. A solution with high alkalinity is able to neutralize more acid than a solution with low alkalinity.
Alkalinity is equal to the stoichimetric sum of the bases (which are maolecules called negative ions - they are short electrons) in a solution. This sum is typically expressed in terms of "molar equivalents" which is the number of moles of each base type multiplied by the the charge of the base ion. A mole is just a fancy science term for the measurement of the amount of a particular molecule.
When it comes to I/A systems, alkalinity becomes an important property. The nitrification process, wherein ammonium ions are converted to nitrate and nitrite, is sensitive to wastewater with low alkalinity. A rough estimate of the amount of alkalinity needed for proper nitrification is about 7mg/L for every 1 mg of incoming ammonium (which is mildly acidic).
In an I/A system, low alkalinity typically manifests itself in high TKN (Total Kjehldahl Nitrogen) results. Unfortunately, Cape Cod and most of southeastern New England has groundwater with notoriously low alkalinity.
Low alkalinity can be corrected by adding sodium bicarbonate (baking soda, NaHCO3) to the system.