Adjectives are words that modify a noun, which helps to better define the subject of the sentence. In the sentence, "The dog barked," you have a complete sentence with a subject, "the dog," and the predicate, "barked." It doesn't give you much information about the dog, though. "The big dark dog barked," then, helps fill in the blanks about what kind of dog actually barked. In an adjective clause, then, adjectives are used in a larger group of words to help modify the noun.
Clauses are a group of words used in a sentence that contain a noun and a verb, and as such can be independent or dependent. An independent clause is something that can stand on its own, rather than "depend" on other parts of the sentence. This can link two clauses together in once sentence. For example, "The dog barked and it scared me." These two sentences could be divided by a period or semi-colon instead of the word "and."
The dependent clause requires other parts of the sentence to be complete and can combine two sentences or independent clauses by combining the two together and omitting one shared noun. A dependent adjective clause might be indicated by the words "who, whom, whose, which and that." For example: "The dog barked and it scared me" could also be written as, "The dog barked, which scared me."
A dependent adjective clause is a clause that cannot stand in a sentence on its own that modifies the shared noun. It generally follows an indicator after the noun in the sentence which replaces the duplicated noun. Sometimes, however, these indicators are implied rather than stated. For example, "The book that I read was a real page-turner," could also be written, "The book I read was a real page-turner."