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To squash the summons, the defendant is asking the Court to make the summons null and void.
This would mean that even if the summons was served, it is not effective service of the complaint, and the Plaintiff is now required to go and get a new summons issued.
The statute in Illinois that you will be working with can be found here: http://law.onecle.com/illinois/735ilcs5/2-301.html
The defendant is objecting to your service for lack of personal jurisdiction (meaning "insufficient service"). However, if you are successful in opposing the motion (prevail in the hearing), they will be forced to file an answer or other responsive pleading.