What is domain redemption and the Redemption Period?
When a domain expires, there is a set process at the registry for a registration to be deleted. This is done to protect owners who have failed to renew their domains on time for a number of reasons. Each registry has different policies and practices relating to expiry, so check the details on the relevant TLD page.
At expiry, the domain enters a Grace period, during which the domain can be renewed at normal rates. There is a separate answer relating to the Grace period.
Following the Grace period, the domain will be marked for deletion. Some registries provide an additional period of time called the Redemption Period, where an existing owner can redeem the domain from the deletion list. The process for doing this is more expensive than a standard renewal and requires considerably more work to undertake. The owner must pay the necessary fees and redeem the domain with exactly the same contact details and registrar as the current (expired) record.
With five days of the end of the Redemption period, the domain is deleted from the register. This means the domain has been put back on the open market and is available for registration by anyone.
Note, not all registries offer a Redemption period and the window for redemption is different for those registries that do offer it. The cost and time required to redeem an expired domain are considerable. Do not rely on the Redemption Period as an option for domains you want to renew.