Diglossia is a situation in which one form of a language (the H variety) is used for formal purposes (writing, speeches, &c.) and another (L) is used for conversation (and is rarely if ever written down); a typical example is Arabic in those countries where a dialect of it is the vernacular. The classic article is by Charles Ferguson (1959), but much work has been done since, and Nancy Gandhi has turned up a useful summary by Harold F. Schiffman. A couple of points:
Difference between Diglossia and Standard-with-dialects. In diglossia, no-one speaks the H-variety as a mother tongue, only the L-variety. In the Standard-with-dialects situation, some speakers speak H as a mother tongue, while others speak L-varieties as a mother tongue and acquire H as a second system.
What engenders diglossia and under what conditions.
(a) Existence of an ancient or prestigious literature, composed in the H-variety, which the linguistic culture wishes to preserve as such.
(b) Literacy is usually a condition, but is usually restricted to a small elite. When conditions require universal literacy in H, pedagogical problems ensue.
(c) Diglossias do not spring up overnight; they take time to develop
These three factors, perhaps linked with religion, make diglossia extremely stable in Arabic and other linguistic cultures such as South Asia.
I might add that Nancy owns a book on the subject that I will have to scour the library for; it sounds very interesting. And that means I’ll wind up delving into Tamil, for which at least I have a Tamil-Russian dictionary.