Since wabi-sabi represents a comprehensive Japanese world view or aesthetic system, it is difficult to explain precisely in western terms. According to Leonard Koren, wabi-sabi is the most conspicuous and characteristic feature of what we think of as traditional Japanese beauty and it "occupies roughly the same position in the Japanese pantheon of aesthetic values as do the Greek ideals of beauty and perfection in the West."
"Wabi-sabi is a beauty of things imperfect, impermanent, and incomplete."
"It is the beauty of things modest and humble."
"It is the beauty of things unconventional."
The concepts of wabi-sabi correlate with the concepts of Zen Buddhism, as the first Japanese involved with wabi-sabi were tea masters, priests, and monks who practiced Zen. Zen Buddhism originated in India, traveled to China in the 6th century, and was first introduced in Japan around the 12th century. Zen emphasizes "direct, intuitive insight into transcendental truth beyond all intellectual conception." At the core of wabi- sabi is the importance of transcending ways of looking and thinking about things/existence. 
Material characteristics of wabi-sabi:
...essential knowlegde, in zen doctrine, can be transmitted only from mind to mind, not through the written or spoken word.
"Those who know don't say; those who say don't know."
Wabi-sabi means freely translated: less-is-more-mood. Historically, it was the origin of a cultural revolution in medieval Japan which opposed the hedonist pomposity of the imperial court with a noble simplicity as the highest virtue and led to the rule of the samurai warriors. As a style-building cultural principle, wabi-sabi proposes a basic tone of typical Japanese feeling: it works in religion as well as in architecture and industrial design, in education, painting and literature. Wabi-sabi directs the view of the becoming and passing away in everything and finds the inner beauty in the externally incomplete, fleeting, transient. The melancholic atmosphere of a rainy day, the patina on copper temple roofs, the wrinkles in the weathered face of a rice farmer, a deliberate deceleration in human life rhythm ... all this is wabi-sabi.
- taken from WABI-SABI: FOR ARTISTS,DESIGNERS, POETS & PHILOSOPHERS, 1994, Leonard Koren