WordPress cannot write files

I have a freshly installed wordpress on my own webserver (nginx). I am getting this problem:

Sorry, but I can’t write the wp-config.php file.

You can create the wp-config.php manually and paste the following text into it.

I do not have FTP server installed, everything that is transferred to my webserver is with SFTP (makes it more secured).

What are the reasons why wordpress is unable to write files on its own? Is it because I need a ftp server? Set permissions? chmod? Maybe I am missing some server configurations? First time running webserver and any help would be nice.