Only the Owner of the discord server/guild is able to delete the server/guild.
How to delete a server/guild
To delete a server as the owner, you will first head to server settings through the server dropdown menu.
Server Dropdown
After you navigate to the server settings page, click on "Overview," which should be the first option displayed.
Server Settings Page
Now that you are in the overview, you should scroll down to the very bottom of the page where the "Delete Server" button is located.
Server Settings -> Overview
If you are confident that you want to delete the server, you will now press the red "Delete Server" button. This will bring up a confirmation pop-up. If you want to continue, press "Yes"; to cancel, press "No".
Server Deletion Confirmation Popup
If you have Two-Factor Authentication (2FA) enabled, Discord will require you to provide your 2FA code before deleting the server. If you do not have 2FA enabled, the server will be deleted with no other confirmations.
Server Ownership is a very dangerous permission to have. We recommend not transferring server ownership to people you do not fully trust for the security of your server(s).