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Underlying Guile's value proposition is the assumption that programming in a high level language, specifically Guile's implementation of Scheme, is necessarily better in some way than programming in C. What do we mean by this claim, and how can we be so sure?
One class of advantages applies not only to Scheme, but more generally to any interpretable, high level, scripting language, such as Emacs Lisp, Python, Ruby, or TeX's macro language. Common features of all such languages, when compared to C, are that:
In the case of Scheme, particular features that make programming easier -- and more fun! -- are its powerful mechanisms for abstracting parts of programs (closures -- see About Closure) and for iteration (see while do).
The evidence in support of this argument is empirical: the huge amount of code that has been written in extension languages for applications that support this mechanism. Most notable are extensions written in Emacs Lisp for GNU Emacs, in TeX's macro language for TeX, and in Script-Fu for the Gimp, but there is increasingly now a significant code eco-system for Guile-based applications as well, such as Lilypond and GnuCash. It is close to inconceivable that similar amounts of functionality could have been added to these applications just by writing new code in their base implementation languages.