This script is included in almost all Linux source, especially for software written in compiled languages such as C and C++. It is used to generate a Makefile (file used by make) that is properly configured for your system. Standard Debian packaging tools use it, so it is important that you know what the configure script does. You do not need to know how to create a configure script yourself, as the software author (or autoconf will do that. However, you may have to adjust it at some point to get a Ubuntu package to build correctly.
First, get the GNU Hello source. From a terminal:
wget http://ftp.gnu.org/gnu/hello/hello-2.1.1.tar.gz # get the package tar -xzf hello-2.1.1.tar.gz # unpack it cd hello-2.1.1/
Now, with ./configure you can run the configure script to generate a Makefile that is customized to your system.
You can also give ./configure command line options. For instance, by default GNU Hello will install to the /usr/local/ directory. You could instead install it somewhere else (a personal binary directory, ~/programs/, for example)
./configure --prefix="$HOME/programs/" # specify install directory.
You can see all the ./configure options by running ./configure --help.
Information on ./configure can be found in the make documentation.