I found out only now, over three years later, that I overlooked responding to the rejoinder above, so I'm taking the opportunity to do so now to bring proper closure to the discussion:
That's right. "That" is a subordinating conjunction. In the complex sentence "He said that he loved her," for instance, "he said" is the main or independent clause and "he loved her" is the subordinate or dependent clause. The conjunction "that" links and subordinates the clause "he loved her" to the main clause "he said."
However, "that" can also function as relative pronoun particularly with reference to animals and inanimate things. In the sentence "They shooed the mongrel that chased my cat," for instance, "that" functions as relative pronoun to refer to the object of the main clause "they shooed the mongrel" as the subject of the subordinate clause "that chased my cat."