I'm using WordPress REST API (Version 2), and I want to authenticate Android native app with my self-hosted WordPress site. How can I perform that using username and password ?
The best way to authenticate an app with the REST API would be to use OAuth. There's a good section on OAuth Authentication the REST API documentation site. You will need to install the OAuth1 plugin on your site as well.
There are some gotchas with implementing the OAuth plugin on WordPress. I found this article on CSS Tricks captured some of the complexity of setting it up.
If your app is just in testing mode, you could use Basic Authentication instead of OAuth, because it's easier to implement, but it's not recommended for production use because it's less secure.