Open enrollment in the Illinois Insurance Marketplace, a part of the Affordable Care Act (ACA, or "Obamacare") begins Sunday, November 1, 2015. You have until December 15, 2015 to enroll and have health coverage begin January 1, 2016. If you do not enroll in a 2016 health insurance plan by January 31, 2016, you can't enroll in a health insurance plan for 2016 unless you qualify for a Special Enrollment Period.
There is a wealth of information available online about ACA; the links below, from the U.S. Department of Health and Human Services and the State of Illlinois, will help answer your questions.
Additional sources of information: