A domain name is basically something that you enter on the browser to access a particular website. For example, to access google search you enter google.com on the browser and it takes you to the search engine. In this case google.com is the domain name for Google Search.
Here's a more detailed information about what a domain name is.
If you're past the tldr section and reading this, you've probably got very little idea about domain names and are eager to know more. If so, this article is dedicated to introducing you to domain names and how they work.
Imagine you've started a new business. You chose a great location in the middle of a city. The location (obviously) has an address. So whenever a customer wants to visit your business, they'll need to know the physical address of the business. If, say, your address is 1 George Street, Sydney the client first reaches Sydney then gets to the George Street then gets to no. 1. At this point your client is at the door waiting to be welcomed.
Now your business is doing well and you start getting recommendations for setting up a website. You designed a great website that showcases your products and services. Now you need a way for your clients to find the web page. Just like you have an address for your business's physical location, you'll need a location for your website. A website's typical address has the format n.n.n.n where each 'n' is a number from 0 to 255. For your website's address could be 184.108.40.206 (called IP address) or any other unique combination of 4 n's. A web browser uses this address to find your webpage. How it finds it is discussion for another article.
Now you might be thinking, it's like a phone number, but for instead a it's website number. Yes! But there's a problem, people aren't good with numbers. You might get an address and publish your website to that address, but people will simply forget that number. This is where domain names come into play. Just like a phone number has a name, each address can have a unique name. For example, you could choose to associate a name for the address you published your website to and when clients hit that name on the browser it takes them to your website's address.
Let's say you chose rumplesbarbershop.com.au as the domain name for your websites' IP address. When the clients now enter this domain name on their browsers they land on your website........ wait.... so just like a phone address, my clients have to save this domain name and it's IP address on their browsers? Actually, NO! This is the beauty of domain names! In case of your phone, your phone directory is stored on the phone memory or sim memory. In case of domain names, it's IP address gets stored on a public server called a Domain Name System Server (DNS Server).
Basic illustration of how domain name system works
A DNS server is like a public directory of phone numbers but for website numbers. Anyone in the world can query this server for a particular domain name's address. I say query because you can only ask for "what is the address for this place?" you can't ask for " a list of all your records". So DNS queries have to be one at a time. So when a client enters your domain name on the browser, the browser first queries the DNS server for the IP address. The DNS Server then replies with the address and the browser then takes you to the website.
Domain names were invented to mitigate the issue of people forgetting the IP addresses so there's no point of having a domain name if you're going to name it very long and difficult. To take full benefit of domain names, it has to be short and easy to remember. Think of youtube.com, or webatmos.com they're short and they're easy to remember. Search engines like google.com constantly crawl the web for content and prioritize domains that are short and meaningful in their search results. So a properly named domain name is very crucial.