The web server operates in a dual-user mode for enhanced security. In order for a web application to access your filesystem, specific permissions must be granted.
Change permissions on necessary files to 717 or 777. For WordPress,
wp-content/themes/ should be changed recursively to allow media uploads and theme editing in-browser. If plugin editing is desired, change permissions recursively on
wp-content/plugins as well.
The same process may be done for any other plugins or themes than require write-access to any folder not covered above.
Important: traditionally, PHP and site files operated under one user, for two major reasons: accountability and ease-of-use. Accountability in that service providers providing unlimited resources can better target accounts that are unsuitable for a truly “unlimited” hosting plan (ie. consuming too many cpu resources). Running all WordPress applications under the same user allows administrators to flag abusive accounts that might lie above a bell curve. Second, it’s easy to update files when all files accessed by the web server are owned by the same user. Permissions are not an issue. Just let the user update WordPress from WordPress’ dashboard and done.
But there’s a huge problem running under one user! Any request on the domain, whether legitimate or forged, can be leveraged by an attacker. Because, the HTTP request assumes the same ownership as you, any PHP exploit can be first leveraged to gain access, then bootloaders (simple file managers) can be injected into any PHP script allowing an attacker to upload malicious scripts elsewhere so long as he knows the special key. Exploits do happen. Update regularly!
By running as a separate user, the window of opportunity to exploit is limited. Only files that you explicitly authorize write access can be modified by a PHP application. If a hacker can’t modify the file, then the hacker can’t inject a bootloader or other malicious code. Only let the web server write to locations that are necessary for operation. Setting permissions to 717 on only those directories/files that are updated regularly by a PHP application is a great solution to reduce your surface exposure. But, don’t set these permissions on all files or your account is just as insecure as running under one user.