switching wordpress website from test to live in plesk

The issue is that your website does not have public DNS records and you should create them.

As you want to host it on Plesk server let me explain on example:
Let's assume that you have created a website and called it example.com. For development and tests you used wamp server on your local machine and to reach website you edited local hosts file.

Now you want to move it to production, so what you need to do:
First you should register your domain. You can do it with some registrar like GoDaddy.

Next you need to create this domain in Pleks > Subscriptions > Add Subscription. On this step Plesk will create a DNS zone for your domain on local DNS server.

After that you have two options:
1. Allow Plesk to host and serve DNS zone. In this case you need to configure Plesk server as name servers for your website on registrar side.
2. Use another DNS server, for example provided by your hosting provider, and configure zone for your website manually.

Finally you need to wait until zone will be propagated world-wide and your website will become accessible.

You can read more about DNS here, here and here.