Like all conjunctions, correlative conjunctions connect sentences, phrases or clauses to one another. They usually have two parts. The first conjunction introduces the first phrase or clause, and the second one introduces the second phrase or clause. Correlative conjunctions are used to connect clauses of equal weight or to join together two independent clauses or two subordinate clauses.

Examples:
Harry denkt sowohl über Julia als auch über das Orakel nach.
Das ist nicht nur gefährlich, sondern auch verboten.

Conjunctions with multiple components, such as "sowohl ... als auch" and "nicht nur ... sondern (auch)" are used to join words or groups of words. The correlative conjunction "sowohl ... als auch" emphasizes the two separate elements (for instance "Julia" and "das Orakel" in the above example) more strongly than if they were joined by a simple "und".
"Nicht nur ... sondern (auch)" often denotes more than just an even comparison. It gives the sense of a progression or escalation.

Example:
Julia ist nicht nur traurig, sondern verzweifelt.

You've already learned some other correlative conjunctions, such as "nicht/kein ... sondern" and "entweder ... oder". "nicht/kein ... sondern" expresses a contrast between two elements and "entweder ... oder" poses them as alternative options.

Examples:
Harry ist nicht mutig, sondern feige.
Sie sind entweder verliebt oder verrückt! Oder beides.

If the correlative conjunctions connect two clauses that share the same verb and/or subject, then it can be omitted from the second clause. That's shorter.

Example:
Harry ist nicht mutig, sondern er ist feige.
Harry ist nicht mutig, sondern feige.

More:

This chart shows you the most common correlative conjunctions along with their meanings.