1. The dog chased the cat.
2. The dog chased the cat that ate the mouse.
In the first sentence, both entities are just regular plain old entities. However, in the second sentence, the object of the sentence has a relative clause attached to it. Now, in this case, what is the purpose of the relative clause? Well, it adds further information about the entity. So, in the discourse of the second sentence, it may be the case that there are two possible cats to talk about, but we are picking out of the two the cat that was involved in eating the mouse.
Relative clauses are one kind of extraction. Relative clauses are made by joining two clauses together, basically. There is a main clause, and the relative clause needs to have a missing argument, since this is basically the same entity as in the main clause. Thus, in the second sentence above, "ate the mouse" is actually the clause with a missing subject.
In many languages, the relative clause either have a missing subject or a missing object. Compare the following two sentences in English.
3. The cat that _____ ate the mouse went missing.
4. The cat that the dog chased _____ went missing.
Sentence 3 has a subject relative clause, while 4 has an object relative clause. So English allows extractions for both places. There are languages, however, that have restrictions on extraction. Tagalog, for example, is one such language where one can only extract the subject of the relative clause. Thus, object relative clauses do not exist in Tagalog. In order to extract the proper entity, one needs to modulate the voice of the relative clause in order to vary the subject, and then one can extract it.
Okay, that last bit must have sounded gibberish, since I am not providing any examples here. But hey, this isn't a research paper, so I guess this is enough. If you really are curious, then email me and I will be more than happy to give you examples and further explanation.