Those seem to be language specific.
Did you see this: http://en.wikipedia.org/wiki/D_with_stroke
Also compare: http://en.wikipedia.org/wiki/Eth

Please refer to Unicode.org for questions like this.

As for the D with bar it’s a bit confusing indeed: there are three different Latin characters with this very glyph:
00D0 »Eth« (Icelandic)
0110 Croatic
0189 African (Ewe language)

As for the D with bar it’s a bit confusing indeed:

It was after viewing the above sources that was just as confused and when I began to research its use.

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As for the D with bar it’s a bit confusing indeed: there are three different Latin characters with this very glyph:
00D0 »Eth« (Icelandic)
0110 Croatic
0189 African (Ewe language)

I don't understand why this is confusing.

Other characters with the same glyph are really confusing, as they may appear in the same document:
0/o, 1/I/l, and apostrophe/quoteright.

I don’t understand why this is confusing.

The question is when do you use this particular glyph if it has so many uses.

off topic: is it just me or has the formatting of this thread changed to italics since my last post?

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I only see one use in three different languages.

I'll admit that I have seen it used as a swash character in English in some heavy metal subway ad. I suppose if you want to use it that way you could, but those in the know would laugh. But then, there are very few "in the know" with regards to this glyph.

The question is when do you use this particular glyph if it has so many uses.

What altaira, Andreas, and terminaldesign are saying is that this character will only come up if you are setting type in one of those three languages. Just like, say, an a with an acute accent -- á -- is used by certain Latin-based alphabets, but not all of them. You wouldn't use it in an English text, unless you had to type a Spanish name or word, for example. Same goes for the eth character.

The reason why there are three different D-bar characters in Unicode is that they each have a distinctive lowercase form:

Ð ð
Đ đ
Ɖ ɖ

Thank you all for clarifying essentially why a character would be used. I believe I have a better
understanding. It was just that Audi uses a ∂ I believe for the d in the name, but I could not understand why if that glyph represents a Ð

So that is why I was wondering when to use a particular glyph namely Ð

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Note the distinction between ð and ∂. The Icelandic lowercase eth has a bar through it, just like the uppercase. The character ∂ is a mathematical symbol with no uppercase form, but it is based on a legitimate variant shape of the lowercase d found in some cursive styles (this is also the normal form of the Cyrillic letter д in most italic styles).

So this is part of their language in that area (Audi). I get it now. It does make for an interesting take on a logo.

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The character ∂ is a mathematical symbol with no uppercase form, but it is based on a legitimate variant shape of the lowercase d

It stands for partial derivative (and hence is sometimes simply called "partial", as in "partial f by partial y" for ∂f/∂y). It contrasts the "ordinary" derivative, which is symbolized by a d, and we say "dee x by dee y" for dx/dy.

No, the ‘d’ in Audi is neither a ∂, a ð nor a đ. Just a regular lowercase Latin d. The form without downstroke used to be pretty common in Germany, as it is the usual ductus in Blackletter (Audi was founded in 1909).
You can find the ‘stemless d’ in other logos (like Jade) and also in a number of non-Blackletter typefaces (e.g. Bello or Cochin Italic).
F

So this is part of their language in that area (Audi). I get it now.

No, you don't. As Florian says, the letter in the Audi logo is just a stylised d. As I wrote, this is a 'legitimate variant shape of the lowercase d found in some cursive styles'.

No idea why, but when I was in Japan I commonly saw hand-written signs for Compact Discs written as "CÐ". I assume it was just stylistic, but it was a common thing to see nonetheless.

I would not assume anything based on what you see in Japan :-) Well, at least not anything in English.

See for example this image my brother took on a vacation.