What does "not for nothing" mean?

Is the meaning of the phrase "Not for nothing" literal, or idiomatic, and if idiomatic, what does the idiom mean? If you have a reference more reliable than urban dictionary, please share it. Here are two quotes using the phrase in which its meaning seems literal:

Not for nothing had he been exposed to the pitiless struggles for life in the day of his cubhood, when his mother and he, alone and unaided, held their own and survived in the ferocious environment of the Wild.
-Jack London

It is not for nothing you are named Ransom.
-C.S. Lewis

However, this phrase comes up all the time in Aaron Sorkin's writing, especially the TV show The West Wing, and its usage there seems more idiomatic. For example:

Not for nothing, but, you know, we're gonna have to get into the thing at some point.

Josh Lyman: We elect these people. And not for nothing, but if we'd been the world's policeman in the thirties, you and I...
Toby Ziegler: We'd have had a lot more relatives.

In the previous two examples, the sentence structure was

"Not for nothing" <verb> <rest of sentence>

but in the last example, the structure is:

"Not for nothing", <but>, <full sentence>

I suspect that the phrase is being used idiomatically in the last example, but I am unsure of the meaning in this context.

In its straightforward "literal" sense, not for nothing is equivalent to for a very good reason.

But lately in the US it's used idiomatically (often followed by but) defined by UrbanDictionary as...

used to soften the blow of something that would normally be offensive or come on too strong.

There's also this Wordpress post giving the meaning “What I’m about to say is important” - which "sorta" makes sense as a "literal" usage (I have a good reason for saying what I'm about to say), though I must admit I've never come across it. But it can be seen as a "bridge" between the literal sense and the otherwise impenetrable idiomatic usage above (I have to tell you this because it's important that you should know it, but I don't want to tell you, because you won't like hearing it).

"Not for nothing" means, literally, "for something," but should be interpreted as "there is a good reason that..." It is used to describe something fitting.

I have always interpreted hearing this as "Naught for nothing," rather than "Not for nothing."

As mentioned above, I can tell you that is it not for nothing that I am typing this response. But the way that I hear people use this phrase is always followed by a "but" and then some opinion or advice.

So I heard it as "naught," and assumed that it meant "I am offering this opinion, and its value is nothing but you have paid nothing for it." Or, "here is nothing in exchange for nothing." You may also just as easily be saying "I know you didn't ask my opinion, but..." or "What I am about to say has no value, but..."

So, this post is "naught for nothing." You may get nothing from it, but you also didn't ask for it or pay anything for it... its nothing for nothing.

Most people who use it, though, likely just use it as a mix of verbal filler and a clumsy way to qualify their opinions to try to cut off any argument about what they are about to say.