We can take the definition from Wikipedia, I feel is pretty accurate:
A style guide (or manual of style) is a set of standards for the writing and design of documents, either for general use or for a specific publication, organization, or field. (It is often called a style sheet, though that term has other meanings.)
A style guide establishes and enforces style to improve communication. To do that, it ensures consistency within a document and across multiple documents and enforces best practice in usage and in language composition, visual composition, orthography and typography.
In the Old School days when the designer was creating the branding identity, besides designing the logotype, stationery, etc, was creating a document. That document contained information about where, when and how use the logotype, what colors and palette, what fonts and family fonts to use, and a big etcetera.
It was a guide to apply the branding identity in all different kind of medias and supports. It was really helpful, specially when the branding identity was in hands of third-party designers.
Nowadays a Style Guide became just something fancy and affordable for big companies, or companies willing to spend in such guide. Seems like nobody asks for a Style Guide when asks for a Logotype. The competition for affordable prices created a jungle plenty of ugly and bad applied designs. You only need to go to Google to see it.
As a Creative I always recommend to develop a Style Guide for my clients, and as a client you should always ask for a Style Guide. Yes, it will be more expensive, but you will be creating the strongest foundation for your brand. And that investment, what can seem big at the beginning, can save you tons of money and “bad” reputation in the future.
We create Branding Identity for our clients, but we create WordPress themes as well. In the same way somebody can ruin a logo just by using it incorrectly, somebody can ruin a theme just by using any of the options from the WordPress Editor. That’s why our themes are created and follow Style Guides as well. We disable and limit options to ensure the theme is always going to look as its best possible.
Here is an example of a Typography Guide Style for our own Portfolio Cards WordPress Theme.