What an assessed value actually is
It is not a fact the county issued. It is an opinion produced by a model, and opinions can be wrong.
Your assessed value is not a measurement. Nobody came to your house, walked the rooms and priced it. In almost every Illinois township it was produced by mass appraisal: a statistical model fed with sales in your area, lot sizes, building sizes, ages and class codes, which then assigns a value to every parcel at once.
Why that matters
A model is a set of assumptions. If the assumptions about your property are wrong — the lot size on file is bigger than your lot, the model thinks you have a finished basement, the sales it learned from were on a nicer street — the output is wrong, and it is wrong quietly. Nothing flags it. The number goes on your notice looking exactly as authoritative as a correct one.
This is not a criticism of assessors. One office may be responsible for tens of thousands of parcels with a handful of staff. Mass appraisal is the only way to do it at all. But a process built to be right on average is not built to be right about you, and the appeal system exists precisely because the legislature knew that.
What follows from it
Because it is an opinion, it can be contested with evidence, and the evidence does not have to be an appraisal. The two most common winning arguments are that the county's record of your property is factually wrong, and that identical properties near you were assessed differently. Both are checkable from public records.
Start by reading what the county thinks it knows about your house. That is on your assessment notice and on your county's parcel page, and a surprising share of appeals are won on nothing more than a square footage that was never right.