IP address?

IP addresses can be spoofed, and changed. A site block can be bypassed.

Spoofing an ip address might not be a good idea. Because an admin might be able to automatically ban spoofed ip addresses, but continuously banning ip address might not be worth it, for some people.

However, an admin can ban everyone, and allow some people to visit his, or her website, and this method of blocking can't be bypassed.

IP addresses do not necessarily change that often. Only your ISP can change your public IP address. Most sites that block by IP also block the low end subnet entirely (to prevent simple re-assign another IP).
You cannot "spoof" an IP address that your ISP controls. You can change your public IP by using a Proxy or a VPN service, but many web sites can detect that and still ban you.

If you have an account at the site, they simply lock the account.

If it is using an installed App on your computer, they can set a flag in the App to indicate that you are blocked.

The most likely mechanism is to install a cookie on your computer that tells the site you are blocked.

IP blocking is not reliable for excluding individuals. However, sites such as Netflix can recognise IP addresses that are used in other countries, and block the addresses that are trying to access material they should not be seeing. This is because Netflix (or similar sites) will have licences to supply shows only in specific countries, and, for legal reasons, they block viewing from countries for which they do not have licences. They will also block known proxy servers to prevent people from using a proxy to get around licence restrictions.

I hope this answers your question.

probably by using the mac address