Here's a typical scenario - you install software from source, spend an hour figuring out the configure options, and finally run:

./configure --prefix=/a/b/c --with-X --with-Y \
  --with-Z-dir=/usr/local/Z --enable-A --disable-B

A year passes by, a new software version has come out, and you want to upgrade. To do that you need to run configure again on the new source code. However you've forgotten what the configure flags were because it's been a year.

If you're lucky, you still have the old build somewhere in your home directory. Here's what you do. You go into the old build directory and run this:

./config.status --config

This will output the exact configure arguments that you used to configure the software. You just saved yourself an hour of work trying to remember all the arguments.