From host to host, different files and directories have permissions that specify who and what can read, write, modify and access them. WordPress may need access to write to files in your content directory to enable certain functions hence this is important.
All files should be owned by your ftp user account on your web server, and should be writable by that account. On shared hosts, files should not be owned by the webserver process itself, sometimes this is www, or apache, or nobody user.
Any file that needs write access from WordPress should be owned or group-owned by the user account used by WordPress. For example, if WordPress is running as the FTP account, that account needs to have write access.
If WordPress is running as a particular account, that account needs to have write access to the file.
It is important to note that WordPress may run as a separate account from the server. If this is the case, the server account needs to have write access.
Some of the used plugins require the /wp-content/ folder be writeable, but in such cases they will let you know during installation. In some cases, this may require assigning 755 permissions. The same is true for
/wp-content/cache/ and maybe
The root WordPress directory: all files should be writable only by your user account, except .htaccess if you want WordPress to automatically generate rewrite rules for you.
The WordPress administration area: all files should be writable only by your user account.
The bulk of WordPress application logic: all files should be writable only by your user account.
User-supplied content: intended to be writable by your user account and the web server process.
/wp-content/ you will find:
Theme files. If you want to use the built-in theme editor, all files need to be writable by the web server process. If you do not want to use the built-in theme editor, all files can be writable only by your user account.
Plugin files: all files should be writable only by your user account.
Other directories that may be present with
/wp-content/ should be documented by whichever plugin or theme requires them. Permissions may vary.