Grammar questions answered: Restrictive and non-restrictive

I asked for some grammar questions, expecting/wanting some softballs. Ha! Not a chance. But I will throw myself to the wolves and try to answer.

Stacey asked-
Here's my question(s): What is a restrictive clause? What does it mean, really? What makes it restrictive?

I ask this, because I have a note that says if I'm using the word "which" in a restrictive clause, I should replace it with "that." It would be a helpful note if I knew what it meant! Hahaha! :)
 Okay, to get very basic, a clause is an element which has a subject and verb, and it can be "independent" (can be a sentence on its own, like This will be a long and tedious explanation), or dependent, (which can't be a complete sentence on its own, like which will be hard to understand). 
 Dependent clauses can be used in many ways in a sentence, like to establish some time or place condition--
When I was young, we used to have to walk three miles uphill to school.
or
Wherever we stay that night, we should get a suite with a view of the river.
"Restrictive" clauses are special types of  "relative" clauses. (A relative clause – I know, this gets arcane, but you know, you say and write these every day, even if you don't know the terms—is a clause which "relate" one thing to another. Forget that—just know that relative clauses start with those relative pronouns—who, which, that, what— and then have a verb, like Relative pronouns, which include "which and who," are how relative clauses start.) Relative nouns are usually "adjectival", modifying a noun (often but not always the subject of the sentence). So they are usually used as "appositives" and tell more about the noun that precedes them:  Governors, who serve a four-year term, are the chief executives of their states.
 You can see there that the relative clause—the appositive—just tells us more about governors. (Not all appositives are clauses—they can just be phrases, like The lady in the red hat ordered the soy latte. But let's not deal with that now. :)
What's important in that example is that it tells us more about ALL governors- that is, the meaning of the noun governor isn't narrowed by the appositive. ALL governors serve a four-year term.
 That is a NON-restrictive clause. It tells us more information about the noun it modifies, but it doesn't "restrict" the noun.

Relative clauses can be restrictive or non restrictive.  That is, they either restrict or don't restrict the noun they modify.

Let's come up with a RESTRICTIVE appositive/relative clause (so many terms! But "appositive" is syntactical—about the role this plays in this particular sentence—while "relative clause" is a grammatical term… well, never mind J).  
A restrictive clause will "restrict" or narrow the meaning of the noun it modifies, like:
Governors who take bribes should be impeached.
In this case, the relative "who" clause "restricts" the noun to a specific and narrow meaning. There are many governors, but in this case, I'm speaking only of the ones who take bribes. I'm not saying every governor should be impeached, only that special group who take bribes (I'm hoping that's a small percentage of them!). The restrictive clause stuck in there actually "restricts" the noun, see.
Now the noun phrase isn't just the single word "governors," but the narrower term "governors who take bribes."

Let's diagram both those sentences:
Subject (noun phrase)
Predicate (verb phrase)
Governors, who serve a four-year term, are the chief executives of their states.
Governors who take bribes should be impeached.
See the difference? Who are the chief executives of the states? Governors. You can take the appositive clause out and the main clause still means what you want it to mean—
Governors are the chief executives of their states.
But see what happens when you take the appositive out of the second one:
Governors should be impeached.
Even if we don't like politicians, we probably don't mean that all governors should be impeached!

So…
Relative clause (who/which/what/that + verb)
Appositive (a clause or phrase which explains more about a noun)
Restrictive clause (a relative clause which "restricts" the meaning of a noun) Governors who take bribes should be impeached. This is NOT set off with commas before and after because it is necessary to the meaning and actually becomes part of the noun.
Non-restrictive clause (a relative clause which explains more about a noun but doesn't restrict the meaning)- Governors, who serve a four-year term, are the chief executives of their states. These are set off before and after with commas, to show that they are "unnecessary" to the meaning.
--
What about "which and that"?
They are both "relative pronouns" which start relative clauses.
"Which" is used in non-restrictive clauses JUST BECAUSE. (I mean, I don't know why.) That means you use commas before "which"—not because it's "which," but because it's non-restrictive, which uses "which".
"That" means exactly the same thing, but is used with restrictive clauses and no commas.
(With people, btw, no matter what, we use "who." Also, my cat, WHO is named Bandit, reminds me we also use "who" with pets.)

Restrictive clause –  Pedestrian malls that are successful share three important factors. (that is, we're only talking about successful pedestrian malls).

(People= who) Pedestrians who cross against the light are taking a big risk. (Only those who cross against the light are taking a big risk.)

Non-restrictive clause -- Pedestrian malls, which limit car traffic on downtown streets, are popular with businesses because they increase foot traffic. (All pedestrian malls are popular with businesses.)

Pedestrians, who are often walking for their health, are tempted by the bakeries which line Ontario Street.

What do you think? Does that make sense?  Often if you speak the sentence aloud, you can tell if you mean the more narrow subject ("Governors who take bribes"), as you will speak that without the pause that would indicate commas.

Restrictive vs. nonrestrictive always gives me a headache to explain, and anyway, it's been explained better by others:
Restrictive_and_Nonrestrictive
Another site for this
Check these out. :)