Open enrollment with regard to Medicare can certainly be confusing. To start, there are different "open enrollments" for the various aspects of Medicare.
Original Medicare Enrollment Periods
Original Medicare (Medicare Parts A and B) has an Initial Enrollment Period and a General Enrollment Period. The initial enrollment period is 7 months, beginning 3 months prior to when you turn 65 and ending 3 months after. If you miss this period, Medicare's General Enrollment Period is January 1 through March 31.
Medicare Supplement Enrollment Periods
Medicare Supplement plans also have an Open Enrollment Period, which lasts for 6 months and starts when you have Medicare Part B and are 65 or older. During this time, carriers cannot ask underwriting questions and your acceptance is guaranteed. Outside this period, you can still apply for a Medicare Supplement plan, or switch to another plan, but underwriting is required.
Medicare Advantage and Prescription Drug Plan Enrollment Periods
Medicare Advantage (Medicare Part C) and prescription drug plans (Medicare Part D) have their own open enrollments. The Initial Enrollment Period for both Medicare Part C and D is identical to the Original Medicare Initial Enrollment Period, but Parts C and D also have an Annual Election Period each year from October 15 through December 7. During this period, you can enroll in or switch Medicare Advantage plans or prescription drug plans.
Finally, Medicare Advantage plans also have an additional Open Enrollment Period from January 1 through March 31 when you can switch to a different Medicare Advantage plan or leave a Medicare Advantage plan and return to Original Medicare (and enroll in a Part D plan).
Outside of these various open enrollment periods, there are "special election periods" that allows you to make changes to your plans. Typically these special election periods are triggered when you lose your current coverage (for example, my moving outside the service area or by retiring and losing your employer plan).