Subordinate clauses are dependent upon an independent clause or another subordinate clause. They cannot stand on their own. Often they begin with certain words (subordinating conjunctions, relative pronouns or question words) that connect them to the superordinate clause. Such connecting words are also known as subordinators or complementizers.

But with some subordinate clauses, the complementizer (conjunction, relative pronoun, etc.) can be left out.

Examples:
Ich glaube, ich bleibe für immer hier.
Ich hoffe, du wirst die nächsten Jahre mit mir verbringen.

Such subordinate clauses are often subject or object clauses derived from "dass" clauses. The conjugated verb shifts from the end of the sentence to the second position, making them look like independent clauses. These clauses often follow verbs relating to saying and telling, thinking and believing, hoping and perceiving.

Examples:
With a complementizer: Ich glaube, dass ich für immer hier bleibe.
Without a complementizer: Ich glaube, ich bleibe für immer hier.

With a complementizer: Ich hoffe, dass du die nächsten 100 Jahre mit mir verbringen wirst.
Without a complementizer: Ich hoffe, du verbringst die nächsten 100 Jahre mit mir.