This literally means "a brand (of clothing) that tells a story" (which actually gets hits on Google), but I think for a better sound you could use "appeal." So the phrase would be "a brand that focuses on (is particular about) good design, quality and appeal."

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Note added at 26 mins (2006-08-02 15:10:52 GMT)
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"Tells a story" in this case would be the idea that you can tell what the person is thinking/feeling by the clothing he/she wears.

I am not familiar with this expression but have pretty good idea. You know Japanese's propensity to using Katakana-English without defening its meaning clearly. This one is just another, and typical example.
However, when I see a site like this, I have to come up with what I have.

http://hexageon.cool.ne.jp/design_tera/tera_story.html

Essentially ストーリー性 means a story about something. In this case it is very likely a story about the company. Its fundamental designing (among others) philosophy, etc.

Hope this helps to narrow down your search for that critical word.

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Note added at 1 hr (2006-08-02 16:38:31 GMT)
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On second thought -- I would like to suggest "tradition". In essence "companty tradition", but you are looking for one word.

ストーリー性 is a marketing buzz word in recent years in Japan. A "story" of a product is a story or background that a customer can relate the product to.

If you are selling tomatoes and display a photo of the grower and a description of where the tomatoes were grown, what fertilizers were used, etc., you are selling tomatoes along with an associated "story." A basketball can be sold with a story that a famous basketball player regularly uses it for practice (see the reference).
From a customer's point of view, a product with a story has more appeal, value, credibility, ....

Like any buzz word, its meaning varies, but I believe this is the basic meaning.

As for English translation, I suggest "associated story" as a safest option like "a brand with excellent design, quality, and a story associated with it."
If the exact meaning is not an issue, I might also go for "product image" or "credibility", depending on the context.

Reference:
商品のマーケティング戦略のセオリーなんだけれども、品質が良い、価格が安いというだけでは商品は絶対に売れることはない。>それに“ストーリー性”が加わらないとブランディングされないから、消費者に対する訴求力がどうしても弱くなる。
エルメスのバッグが、フランスの国立技術専門学校のトップクラスの出身者の中から選び抜かれた極々限られた名職人だけが全て>の工程を何ヶ月もかけて手作りで制作する、というストーリー性があるからブランド化されたのと一緒。ケリーバッグだって、あ>のグレース・ケリーがモナコ公妃として妊娠を悟られないようにするために持っていたという物語があるから売れるようになった>のである。
http://72.14.235.104/search?q=cache:JNRLJWrDCdMJ:d.hatena.ne...


Note:
Another important meaning of ストーリー性 as a marketing term is a presentation technique of organizing information as a story rather than simply dumping out unrelated bits of information.


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Note added at 9 hrs (2006-08-03 00:19:18 GMT)
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Just ignore "(see the reference)" in the second paragraph.

another suggestion.

See:
http://64.233.183.104/search?q=cache:rUeNhX-zmw8J:www.costum...

Accurate and thoughtful costume design supports the "narrative" and creates characters that...

HTH.