[Vuejs]-How Nuxtjs auth module works exactly?

The auth module uses various methods to authenticate users.
You can integrate a project that you have developed using nuxtjs using one of the items supported in the auth package and perform authentication and authorization operations on your project. For example, you can use this module and Laravel project as backend to handle the authentication discussion in your project.

In fact, your question was very general, I suggest you read the main documentation of the module from the link below.
https://auth.nuxtjs.org/