Guile was conceived by the GNU Project following the fantastic success of Emacs Lisp as an extension language within Emacs. Just as Emacs Lisp allowed complete and unanticipated applications to be written within the Emacs environment, the idea was that Guile should do the same for other GNU Project applications. This remains true today.
The idea of extensibility is closely related to the GNU project’s primary goal, that of promoting software freedom. Software freedom means that people receiving a software package can modify or enhance it to their own desires, including in ways that may not have occurred at all to the software’s original developers. For programs written in a compiled language like C, this freedom covers modifying and rebuilding the C code; but if the program also provides an extension language, that is usually a much friendlier and lower-barrier-of-entry way for the user to start making their own changes.
Guile is now used by GNU project applications such as AutoGen, Lilypond, Denemo, Mailutils, TeXmacs and Gnucash, and we hope that there will be many more in future.