Halliday & Matthiessen (2014: 463-4):
In this case the secondary clause clarifies the thesis of the primary clause, backing it up with some form of explanation or explanatory comment. … The clarification often involves a shift in polarity … The clarification may be an evaluative comment. …
Expressions such as in fact, actually, indeed, at least are common in this type; the nearest written abbreviation is again i.e., or sometimes viz. The conjunctives are cohesive rather structural markers of the paratactic relationship …
Very often the two clauses are simply juxtaposed. This often makes it difficult to decide, in spoken language, whether they form a clause complex or not; but if the intonation pattern is repeated so that there is tone concord, and the semantic relationship of elaboration is clearly present, this can be taken as a criterion for treating them as forming a nexus. In written language the apposition may be signalled by a special punctuation mark, the colon; but this is a fairly recent innovation, never very consistently used, and the lack of any clear structure signal is no doubt the reason why the abbreviations i.e., e.g. and viz. were first introduced and why they continue to be used today.