That is a list of directories. They are seperated by colons (you know, ":"). You can include things from any of those directories or subdirectories thereof. A dot (".") means "the current directory", so you can put includes in the same directory as the files that include them.
Specifies a list of directories where the require(), include() and fopen_with_path() functions look for files. The format is like the system's PATH environment variable: a list of directories separated with a colon in UNIX or semicolon in Windows.
The default value for this directive is . (only the current directory).
I don't believe so, if you give just a file name like so
I think it looks in the specified dirs from the include_path, but if done as so
include $DOCUMENT_ROOT . "/header.html";
I believe it would look in the path specified by your include because the path is absolute, not relative. Not 100% sure, but that is my informed guess.
I noticed, while poking through the fusebox source for PHP, that there is also a chdir function, that lets you change the directory that you are relative to.
example: You start generally in your /public_html(or /www or whatever). But for security reasons, you drop your file with db password et al, to a directory outside of your webroot. You can chdir to that directory, and all your include's are local! (no explicit pathing)
Just remember to take note of where you are before you move, in case you want/need to go back.