What don't you understand exactly?
For instance this sentence: "Some software packages allow you to specify, at compile-time, separate
locations for installation and for run-time".
It is stow which allows to have separate locations for installation and run time, not the package.
When I do:
./configure --prefix=/usr/local/stow/package
make
make install
cd /usr/local/stow && stow package
I have specified the location of the package at compile time, and stows allows to run this package in a different location (/usr/local/stow/package VS /usr/local).
Another thing I don't understand is the GNU Emacs example.
The documentation mention the "new" prefix, but never the old prefix. So I don't know which is the value of the old prefix, and which is the value of the new prefix.
Finally, I don't understand how is it related to this thread.