At the time, Kaskaskia served as capital of the Illinois territory. The Constitution was ratified when Illinois became the 21st state admitted to the Union. Kaskaskia served as the state capital until 1819, when Vandalia became the state capital until 1839.
Today, of course, the state capital lies in Springfield, which we recently visited in this post.
Here is a link to a nice little post about Illinois' state capitols.
The preamble to this Constitution reads:
THE people of the Illinois territory, having the right of admission into the general government as a member of the Union, consistent with the constitution of the United States, the ordinance of congress of 1787, and the law of congress approved April 18th , 1818, entitled "An act to enable the people of the Illinois territory to form a constitution and state government, and for the admission of such state into the Union, on an equal footing with the original states, and for other purposes;" in order to establish justice, promote the welfare, and secure the blessings of liberty to themselves and their posterity, do by their representatives in convention, ordain and establish the following constitution or form of government; and do mutually agree with each other to form themselves into a free and independent state, by the name of the State of Illinois. And they do hereby ratify the boundaries assigned to such state by the act of congress aforesaid, which are as follows, to wit: Beginning at the mouth of the Wabash river, thence up the same, and with the line of Indiana to the northwest corner of said state; then east with the line of the same state, to the middle of Lake Michigan; thence north, along the middle of said lake, to north latitude 42 degrees and 30 minutes; thence west to the middle of the Mississippi river, and thence down, along the middle of that river, to its confluence with the Ohio river; and thence up the latter river, along its northwestern shore, to the beginning.Succeeding Constitutions were ratified in 1848, 1870 and 1970.