In the context of climatology, the word “normal” refers to the 30-year average of selected climate variables (e.g., temperature and precipitation) that is updated every decade. The current set of normals cover the period of 1981-2010. They are a standard and convenient benchmark for comparing conditions between stations and for putting current conditions into prospective. For the record, this convention was established some 75 years ago by the International Meteorological Organization (now the World Meteorological Organization) with the mandated computation for the 1901-30 period. The National Center for Environmental Information has detailed background information on climate normals.
Of course, the average of a variable only tells you one piece of information. Looking at the extremes and other statistics can give you a better idea of what to expect from the historical climatology of a region.
The climate normals for Illinois can be found on these pages: