From the Kodokan:
http://kodokanjudoinstitute.org/en/beginner/about/What images was the Kodokan symbol derived from?
The red circle expresses an iron-core that is fired, and the white outward means the floss silk that wraps the core. The floss silk is pure white and has toughness although it is soft. The more one forges iron, the more it becomes strong.
The symbol expresses the idea that Kodokan members should always have the following spirit: Soft-outward and hard-inward. That is to say, they should have a mighty heart and strengthened physical ability while they behave softly, calmly and rightly to others.
The symbol was made in 1940 improving a symbol that was set by Kano Shihan in the early days of Kodokan. It expresses the spirit of soft-outward and hard-inward. The flower-shaped outward expresses a flower shaped mirror that means trainees should have always Shihan's words in their mind.
From Judoinfo:
http://judoinfo.com/kdk.htmAlthough this is the most widely-publicized interpretation of the Kodokan symbol in the west, it is not the most accurate account. A cherry blossom (sakurabana) in Japanese crests is always represented with five petals, as shown in this symbol and photo of a cherry blossom. By contrast, the Kodokan emblem has eight pointed lobes. Some judo clubs and organisations have used the five-lobed cherry as part of their emblems, and as a meaningful Samurai symbol it is also accepted. But the Kodokan symbol has different origins. The colors in the symbol worn by members of the Kodokan represents a piece of red hot iron surrounded by pure white floss silk -- hard in the centre, soft on the outside. The badge emphasizes the judo principle that the soft controls the hard, or gentleness can control force, that one can win by using the opponent's force against himself.
The Kodokan symbol was not used until after Jigoro Kano died, so he may not have been involved in selecting it. A small pamphlet purportedly published by the Kodokan explained that the current Kodokan symbol was introduced in October 1940, and that the form is modeled after an ancient 8-sided copper mirror (called yata-no-kagami). This mirror is chronicled in Japanese Shinto legends and the shape is represented in numerous Japanese crests (mon). The mirror, reflecting everything truthfully, is a symbol for honesty. The red circle in the center was intended to symbolize a sincere and passionate mind. This historical account is now accepted as the authentic origin of the Kodokan symbol, and it has been confirmed by the Kodokan (Naoki Murata, director of the Kodokan Museum).
The Kodokan symbol is the representation of Yata no Kagami, or "The Mirror Yata" or "The Octagonal Mirror". According to the mythical history of Japan, the Gods offered three sacred gifts to the first japanese emperor to prove his "divine descendence":
KUSANAGI NO TSURUGI - "The Sword Kusanagi"
YASAKANI NO MAGATAMA - "The Jewel Yasakani"
YATA NO KAGAMI - "The Mirror Yata"
The Yata no Kagami is not a normal mirror. Unlike normal mirrors that reflect our external image, Yata no Kagami reflects our soul. For this reason, there are always mirrors inside Shinto temples (it is said the original Yata no Kagame still remains untouched inside a Shinto temple in Japan). Applying Shinto concepts in the symbol of Judo, the white color of Yata no Kagami represents the Judoka's search for purifying his/her soul, and the red sun in the middle stands for the virtues of Judo which the Judoka should focus on..
