When it comes to design, the Greeks and Romans gave us mathematic and geometric perfection. This is starkly different from the contribution of the Japanese, particularly their notion of wabi-sabi, which is both a philosophy and an aesthetic. The term is just about impossible to cleanly translate into English, and instead must be described with a number of words that can seem confusing: Natural flaws, imperfection, assymetry, patina. Roughness, irregularity, impermanence, mortality.
A broken chair you have repaired with a visible splice can be said to possess wabi-sabi. The pattern of rust on an old bicycle, a handrail worn smooth from years of use, the patina on a favorite hand tool, all of these things have wabi-sabi too.
Perhaps the best way to grasp this concept, and hopefully integrate it into your own designs, is to learn the history of the philosophy, where it came from, and how it was first incorporated into the design of physical objects and spaces. There are entire books written on this subject, but we've located a well-edited video that sums it up nicely: