What does "write access for the process that writes to that directory" mean?

Uhm, it means just that. At one moment in time, the server receives an HTTP request, and it contains the content of a file. Somehow, this file needs to be written to disk. This can be done by the server (or one its children), for instance because mod_perl is used. Or the server can hand it off to a different process (for instance, because CGI is used). Anyway, eventually, there is a process that will do the writing. That process needs to have write permission in the directory.

Abigail