Help with permissions

I have a few questions about permissions. I’m reading a lot online but it isn’t really helping me (I’m thick headed).

I have an swf and it’s sending some data to a php file to be written into an XML file. It works perfectly right now, the XML file is 0666 and the php file is 0644.

Now this is what I don’t understand. What is the definition of executing a file? I thought posting some data to a php file and having it write to various files would be considered executing?

Also, if a file is user writable what does that mean? Can someone remotely write to that file from a php script located on another site.

Basically my questions are;

  1. Whats function require execute permissions?
  2. Do public write permissions mean people can remotely write to my files?