An extension language is a programming language interpreter offered by an application program, so that users can write macros or even full-fledged programs to extend the original application. Extension languages have a C interface (it is usually C, but it could be any other compiled language), and can be given access to the C data structures. Likewise, there are C routines to access the extension language data structures.
This uses GNU extension language - Guile (which can stand for _GNU Ubiquitous Intelligent Language Extension_). Guile started out as an embeddable Scheme interpreter, and has rapidly evolved into a kitchen-sink package including a standalone Scheme interpreter, an embeddable Scheme interpreter, several graphics options, other languages that can be used along with Scheme (for now just _ctax_ and _Tcl_), and hooks for much more.