This is a term that denotes the 'umbrella' tradition of Nihon Budo (Japanese martial arts) from which SYR and many other schools descend. In fact, most modern (gendai) Japanese martial arts (and many older koden ryuha) come directly from this strain of martial tradition. For example, Judo and Aikido come directly from this strain of tradition, and so the technique names and structure of these martial arts derive from Takagi-kukishinden. Most forms of karate are directly related to shotokan, and shotokan is directly related to kodokan (judo) and hence most forms of karate (Okinawan and Japanese) bear direct relationship to Takagi-kukishinden and likewise their technique names and structure somewhat descend from this strain of tradition.
Since shotokan is thus inter-related, and was the primary source of inspiration for Korean karate, many forms of Korean karate (tang soo do, kong soo do and etc) and also the Korean arts of Yudo and Hapkido bear direct relationship to this strain of tradition -- and sometimes the Korean terms for techniques descend from it -- but spoken in Korean language.
Most nomenclature for techniques, methods and practices in the modern martial arts come right out of the takagi-kukishinden strain of tradition, somewhere along the line. Most theories, principles and conduct in the modern martial arts come right out of the takagi-kukishinden. If you see it in the martial arts (eastern or western versions, any nation): there is an 85% chance that it came right out of the takagi-kukishinden somewhere along the line -- whether its a technique or a technique name, a principle, practice or custom... chance is that it came right out of the takagi-kukishinden.
Hence the takagi-kukishiden martial arts are highly relevant to all modern martial arts (CJK and otherwise.) Takagi kukishinden is very old, it seems to have originated around the 1500's, according to Japanese historical records. Takagi and Kuki are both family names, the families whom originated the tradition and consequently still exist as families in Japan but these traditions are no longer solely in their possession: The Takagi-kukishinden strains of martial technique are the single most common form of fighting art in all of Japan (and, truthfully, throughout the world.) As a matter of fact, despite being the surnames of these families, the term Takagi-kukishinden has an interesting meaning (and believe me, it's no coincidence).
Takagi-kukishinden quite literally means:
The Traditions of Nine Demons in a Tall Tree.
This was explained to me to have the following meaning: Nine demons (actually, the word 'ogre' or 'goblin' is far more accurate but it always gets translated as 'demon') and one tall tree makes ten (slots or items). The tree represents 'family tree' or 'family line' and so on one hand, it's sort of like saying: "Everybody gather around the family and protect it." [Back in the old days, society was much less stable and reliable -- so that was something one might wanna do, if you know what I mean.] However, it also indicates 9 paramilitary arts used to protect the family with. Since it depicts ten items (nine demons and one tree): it means a 'complete system'.
It is common for the Japanese, and the exponent schools and systems of this martial tradition, to display a symbol which is literally a graphic depiction of the takagi-kukishinden: Nine tengu goblins flitting about in the branches of a tall willow tree. Usually the tengu are shown with swords drawn. This is the graphic depiction derived from the meaning of the combined family names.
Takagi-kukishinden: the Traditions of Nine Demons in a Tall Tree.