In Her father died when she was very young,. we have:

Her father died (main clause)

when (subordinating conjunction)

she was very young (adverbial clause)

A complex sentence consists of an independent clause (simple sentence) and one or more dependent clauses (subordinating clauses). The dependent clause is introduced by either a subordinate conjunction (for an adverbial clause) or a relative pronoun (for an adjectival clause).

1. Some common subordinating conjunctions (adverbial clauses): after, (al)though, as, because, before, if, once, since, unless, until, when, while

2. Relative pronouns (adjectival clauses): who/that, whom, whose (people); that, which (animals, things).