Refined, elegant, or graceful — having a cultivated, tasteful manner or bearing.
彼女の立ち居振る舞いはとても奥ゆかしい。
Her manner of conduct is very graceful and refined.
奥ゆかしい着物の着こなしが好印象を与えた。
The tasteful way she wore the kimono left a good impression.
Modest, reserved, or self-effacing — indicating a restrained and unpretentious demeanor.
彼は奥ゆかしい性格で、決して目立ちたがらない。
He has a modest character and never seeks to stand out.
奥ゆかしさは日本文化で尊ばれる美徳の一つだと言える。
One could say that modesty (a refined reserve) is one of the virtues esteemed in Japanese culture.
その女優の奥ゆかしい態度が観客の心を掴んだ。
The actress's modest and graceful demeanor captured the audience's heart.