What happens when a domain expires

It depends?

I know that feels a bit like a cop-out answer but it all depends on the domain extension you use, the registrar and how popular your domain is, but let's go through a typical scenario.

Domain Grace Period

Typically, once expired, a domain will enter a grace period before it goes back on the market. During this time you can renew it with your registrar (You may have to pay an additional fee).

The Open Market

After the grace period, the domain will usually enter the open market and anyone can snap it up.

If your domain has some links and authority you can guarantee that it's already on multiple lists and in dropcatch baskets.

Drop catching

There is a reasonably large industry of services that check multiple times a second for a domain name to drop, you can back order these (and they get very competitive).