Trying to learn as much as I can.
As Dennis Bruns correctly stated, the differentiation is not about a “high language”, i.e. court or magisterial language, as opposed to a lower, vulgar form like is the case with Latin.
Additional confusion stems from the fact that in German the term “Hochdeutsch” is often used when speaking about “Standard German” or to give its correct name “Standardhochdeutsch”.
In English the term “High German” usually denotes what Germans call “Hochdeutsche Mundarten”, “High German dialectics”, which is the term for German variants spoken south of the “Uerdinger Linie”.
In this context the differentiation is indeed primarily about elevation, with Low German, often called “Flat German”, Plattdeutsch in German, being the language of the North German flatlands and High German being the language of everything that is not the flat plain in the North.