Medigap is Medicare Supplement Insurance, which is sold by private entities and helps fill "gaps" in Original Medicare. Initial Medicare covers a significant part of the cost of eligible health care facilities and equipment, but not all of them. A Medicare Replacement Insurance (Medigap) program may assist with some of the remaining medical expenses, such as: Copayments, Coinsurance & Deductibles.Some Medigap programs often include facilities not provided by Original Medicare, such as medical treatment while traveling outside the United States. Here's what happens if you have Original Medicare and purchase a Medigap policy: For covered health-care costs, Medicare would pay its share of the Medicare-approved total. After that, the Medigap strategy kicks in.