A clause is a group of words that contains a subject and a verb:

She promised.
[This is an independent clause.]

Although she promised
[This is a subordinate clause introduced by the signal word 'Although.']

Independent clauses contain a subject and a verb and they can stand on their own as sentences.

Subordinate clauses contain a subject and a verb, which are introduced by special words called subordinators.

While I paced softly on, the last sound I expected to hear in so still a region, a laugh, struck my ear (Bronte, Jane Eyre, 105).

Although the royal princes and high nobles remained standing, each bowed low to the Great King and kissed his own right hand (Vidal 63).

Relative Clauses modify nouns and sometime indefinite pronouns:

A. Relative clauses are introduced by relative pronouns (that, who, which, whom, whose):

Let me have no happy fortune that brings pain with it, or prosperity which is upsetting to the mind! (Euripides, Medea, 78).

That he [George III] failed in the central problems of his reign may, in the long run of events, have been fortunate for the ultimate liberty of England (Churchill 152).

Still steadily rising, we passed over a narrow granite bridge and skirted a noisy stream, which gushed swiftly down, foaming and roaring amid the grey boulders (Doyle 56).

Partly it came no doubt from his own masterful nature, which loved to dominate and surprise those who were around him (Doyle 147).

The other (the sentiment) is a desire that punishment may be suffered by those who infringe the rule. There is involved, in addition, the conception of some definite person who suffers by the infringement; whose rights (to use the expression appropriate to the case) are violated by it (Mill 308).

Destruction light upon the wife who herself plays the tempter and strains her loyalty to her husband's bed by dalliance with strangers (Euripides, Hyppolytus, 180).

Of the Six, I was particularly interested in Gobryas, a tall, slightly stooped man whose hair and beard had been dyed blood red (Vidal 63).

In all of the above examples, a relative pronoun not only introduces the clause but also functions as the subject or signals the subject that performs the action. Therefore, by having an identifiable subject and a conjugated verb, the group of words is no longer just a disparate set of words, but a grammatical clause. The most important point to remember is that, in contrast to a phrase, a clause must include a subject and a conjugated verb. Take Gore Vidal's example (immediately above): 'whose hair and beard' is the subject as introduced by the relative pronoun 'whose,' and 'had been dyed' is the conjugated verbs.

B. Relative clauses may also be introduced by relative adverbs (when, where, why):

It is natural for men to err when they are blinded by the Gods (Euripides, Hyppolytus, 220).

When the train came in from Faversham, where he knew Rose had to change, he ran along it excitedly (Maugham 69).

Master writers combine both groups of introducers (relative pronouns and relative adverbs):

When Anaxagoras was condemned, he [Socrates] became a pupil of Archelaus the physicist; Aristoxenus asserts that Archelaus was very fond of him (Diogenes Laertius 149).

Note how the writers of our Declaration of Independence employed the two groups of relative clauses:

When in the course of human events, it becomes necessary for one people to dissolve the political bands which have connected them with another, and to assume among the powers of the earth the separate and equal station to which the Laws of Nature and of Nature's God entitle them, a decent respect to the opinions of mankind requires that they should declare the causes which impel them to the separation.

Adverbial Clauses are introduced by adverbial subordinators (also called subordinating conjunctions); for a complete list of these conjunctions refer to page 41. Adverbial clauses modify the independent clauses to which they are attached, by acting as adverbs. That is right. An entire clause -adverbial clause, made up of several or many words- may act as a regular adverb (which is just one word).

Because it's rare and expensive, I bought it for you.

I bought it for you, because it is rare and expensive.

'Because' is the subordinating conjunction or adverbial subordinator that introduces the adverbial clause, followed by the conjugated verb 'it's.' This adverbial clause gives the specific reason as to why the subject 'I' bought the item. Not only do adverbial clauses give specific reasons for specific actions (expressed by the verb), but they convey all kinds of information in which the subject engages in: they convey time, place, manner, degree, comparison, purpose, result, condition, concession, and cause).

Nominal Clauses are introduced by subordinating conjunctions (how, that, what, when, where, whether, which, who, why); therefore, they are subordinate clauses.

Whether the context is Greek, Christian, or undefined, tragedy seems to lead up to an epiphany of law, of that which is and must be (Frye 208).

What the poet meant to say, then, is, literally, the poem itself; what he meant to say in any given passage is in its literal meaning, part of the poem (Frye 87).

What man loses by the social contract is his natural liberty and the absolute right to anything that tempts him and that he can take; what he gains by the social contract is civil liberty and the legal right of property in what he possesses (Rousseau 65).

Where rights and freedom are everything, inconveniences are nothing (Rousseau 142).

Moreover I saw here under the sun that, where justice ought to be, there was wickedness, and where righteousness ought to be, there was wickedness (Ecclesiastes 3:16).

Retired. Former investment banker, Columbia University-educated, Vietnam Vet (67-68). The only writing textbook I consult is Mary Duffy's e-book: Sentence Openers. This book will fire up your writing. Check it out! To read my book reviews of the Classics visit my blog: Writing To Live http://writingtolive.com/.