A custom domain determines the URL that will be used by the users to access your site.
You'll want the users to access your site via a specific URL that is also your site’s unique identity. For this, you'll need to purchase a domain from a third-party domain authority and point it at your site. Check out Adding a Custom Domain for more details on how you can do this.
For instance, let's say you created a Mindspun site named example, you may then purchase a domain for that site such as example.com and configure that domain to go to your site. Configuring a domain is done via DNS settings carried out by your domain name service providers.
Fun fact: example.com and example.org are often used for documentation (such as this!) and testing, but are not - and can't be - owned by anyone. The curious can read more here.