"Iki" is a traditional aesthetic ideal in Japan. The basis of iki is thought to have been formed among commoners (chounin) in Edo, pre-modern Tokyo. Among those who are not familiar with Japanese culture, some tend to misunderstand iki as simply "anything Japanese." Iki, however, is one of Japanese aesthetic ideals and requires specific conditions. Samurai are typically thought as devoid of iki. The term got its widespread in modern intellectual circles of Japanese through the book The Structure of "Iki" (1930) by Kuki Shuuzou.
While other Japanese aesthetic ideals, such as wabi-sabi, are almost extinct in today's Japan, iki is widely applied today. An average modern Japanese would find it difficult to translate what wabi-sabi means into English, because its definition relies on certain cultural assumptions. Wabi-sabi continues to influence Japanese culture, although its influence is far less than in pre-modern times. On the other hand, iki is commonly used in conversation or publications.
An iki thing/situation would be simple, improvised, straight, restrained, temporary, romantic, ephemeral, original, refined, inconspicuous, etc. An iki person/deed would be audacious, chic, pert, tacit, sassy, unselfconscious, calm, indifferent, unintentionally coquettish, open-minded, restrained, etc.
An iki thing/person/situation cannot be perfect, artistic, arty, complicated, gorgeous, curved, wordy, intentionally coquettish, or cute.
Iki can be used for almost anything, but especially for people (and their personality and deeds), situation, architecture, fashion, design, etc. It always describes something to do with people, or their will. Iki is not found in nature itself, but can be found in the human act of appreciating the beauty of nature.