Question: Why do we have to pay for a domain name if the web is free.
Answer: Yes. The services; most of them; provided by the world wide web is free.Domain names are the building blocks of the world wide web. They act like 'markers' for websites. They are just names, identities(you can say).They need to be pointed to a server(that actually hosts your data; your website in simple terms).
There are four important aspects here:
1) The Registry: The Registry is an entity that manages TLD(Top level domains like .COM,.NET). The registries need to be accredited by ICANN in order to sell domain names for TLDs or ccTLDs. Verisign is a registry for .COM and .NET domain names.
2) The Registrars: The Registrars tie up with various registries to sell domain names belonging to multiple TLDs, ccTTLDs under one roof.For example: Godaddy is a registrar.
3) The Registrant: The Registrant in this case would be you, that is the person who registers a domain name for a fixed period of time(usually 1-10 years).
4) ICANN: The ICANN is responsible for managing this entire process and acts like a regulatory body.
Now the big question: Who do I pay?*Answer:* When you register a doamin name, you pay a major portion of the domain name registration fee to the registrar(Godaddy for example). A very small portion of this amount is paid to the Registry(for example Verisign). The domain registration cost includes this minor amount.
Why do I have to Pay?Answer: This is similar to any other business that is done in order to earn money.As the Internet started growing, people thought of this system to make money.(just like any other business)-Earlier, websites were accessed using the IP addresses.Read about Hosts.txt file if you want to know more.You can also read about DNS, DNS resolution process.