It is hard to explain
Wikipedia tells us that the current meaning of Wabi connotes rustic simplicity, freshness or quietness, and can be applied to both natural and human-made objects, or understated elegance. It can also refer to quirks and anomalies arising from the process of construction, which add uniqueness and elegance to the object. Sabi is said to be beauty or serenity that comes with age, when the life of the object and its impermanence are evidenced in its patina and wear, or in any visible repairs.
The book, Wabi Sabi by Mark Reibstein (Author), Ed Young (Illustrator), says that wabi sabi is a way of seeing the world and allows us to experience that feeling by following the journey of a little cat who sets out to find the meaning of her name.
In their own words
I very much enjoyed the book, even though I sense that my mind is wired such that I may not fully grasp a philosophy that is so deeply rooted in another culture. But, perhaps, that is wabi sabi in itself.
Anyway, I also suggest watching this short video of the author and artist talking about the process of creating the book.