If a domain isn't renewed by its expiration date, here's the sequence, plainly:

First, the domain typically stops resolving; the website and any email tied to that domain go down, usually right around the expiration date or shortly after.

Second, the domain isn't immediately available to anyone else. It moves through the stages described in The Domain Lifecycle, Explained and Grace Period vs. Redemption Period vs. Pending Delete: grace period, then redemption period, then pending delete, each with a real window of time before it's gone for good.

Third, recovering it gets more expensive the longer it's been expired. Once it reaches pending delete, it can't be recovered at all by the original registrant; the only option at that point is waiting for it to release and trying to register it again like anyone else, with no guarantee of success.

If you'd rather not let a domain drift through this process at all, deleting it outright is a separate, deliberate option; see Delete a Domain.