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. The National Center for Environmental Information (NCEI) has detailed background information on climate normals.
But the normals are more than a simple average. NCEI has procedures in place to deal with missing and suspect data values, merging of stations, and making sure that the daily normals add up or average the monthly normals, etc.
Normals are a standard and convenient benchmark for comparing conditions between stations and for putting current conditions into perspective. 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.
Of course, the normal or average of a variable only tell 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: