In short, domain authentication allows servers of the world to know that the email address you use to send emails is really yours. And for you, your email is less likely to bounce or end up in your readers' spam boxes. This can sometimes be a bit of a hassle, but you only have to do this once and the benefits outweigh the costs.
To start the authentication process, go to the top right drop-down menu and click Authentication. The standard settings should work fine if you don’t have access to your current domain. However, if you want that extra delivery boost, check "I’ll manage my own authentication".
Here, you can add one or more domains that you are planning to send from MailerLite. Make sure you add your domain without the www or http://. Just a plain mailerlite.com, for example. After you finish adding your domain, you will be presented with a screen of records that you may have to send to your domain provider. If you have trouble understanding these records, contact your domain provider or us.