The purest definition is that the buyer of a secondary market annuity is purchasing the right to receive the contractual guarantees (typically in payment form) from the original annuity policy.
These types of annuities are initially issued after a person has had an accident and they receive a favorable judgment that involves guaranteed annuity payments as part of the settlement. Some of the inventory also comes from lottery winners. When you buy a secondary market annuity, you are literally buying the right to receive those payments from the existing in force policy.
The original owner will sell some or all of their annuity payments because they need or want a lump sum faster than the payments they are receiving. This could be due to health reasons, financial hardship, an unforeseen expense, the need to buy a home, or to start a business.
This process allows investors to purchase insurance grade products that may carry the same guarantees and protections of the originally issued instrument, however by virtue of the fact that it is being purchased at percentage of its full value, the internal rate of return realized by the investor may be substantially higher than other fixed income products; many times returning as much as 7% fixed annually.