Domain Lifecycle
To understand more about how it works, here's a quick recap of the typical lifecycle of a gTLD domain name:
Image courtesy of ICANN.
When a domain expires, most of the time it enters what is known as a Grace Period. The Grace Period typically lasts between 0 and 32 days and often does not have any additional costs associated with it allowing a domain name to still be renewed at the regular rate.
When the grace period elapses after 32 days, most domains then enter a final status of Redemption. Redemption is the last chance to renew a domain before it becomes available for registration again and often coincides with registries putting the domain up for auction.
Domains can still be renewed while in the redemption status (providing it hasn't been auctioned off) by paying a redemption fee plus the regular renewal cost for the domain.