I thought this was one place the definitions did a pretty good job:
Separately Derived System. A premises wiring system whose power is derived from a source of electric energy or equipment other than a service. Such systems have no direct electrical connection, including a solidly connected grounded circuit conductor, to supply conductors originating in another system.
So, it's a source other than the service....
most often supplied by a generator, transformer, battery, etc.
where none of the conductors connect to conductors of another system.
In the simplest of forms, a doorbell transformer. The secondary windings of the transformer have no connection with the primary.