In some contexts, the Triskele has been associated with spiritual and mystical themes, representing the interconnectedness of mind, body, and spirit or the journey of self-discovery and enlightenment. Evolution and Progress Many HYDRA operatives, including Grant Ward and Skye, worked in an open-space with individual boxes where each operative had their own computer. The place also featured briefing rooms. An episode of Star Trek, The Gamesters of Triskelion, takes place on the alien planet of Triskelion. But sometimes a much deeper spiritual meaning was attached to the Triskelion, being seen as representing:

Clathrin, a protein involved in the formation of endocytic vesicles in most cells, has a triskelion shape. In the Bavarian town of Füssen, Germany the flag and coat of arms of the town contains a triskele, [21] [22] as does the flag of the Russian autonomous region of Ust-Orda Buryat Okrug. [23]After completion, the Triskelion served as the primary headquarters of S.H.I.E.L.D. and housed many of its agents and operations. When it is displayed in tattoo form, the meaning doesn’t change. It just depends on what variation that person takes from it. Can you interpret the Celtic Triskele as a symbol for strength? Whatever the motif’s meaning and symbolism, or perhaps precisely because of its symbolic flexibility, it was a prominent symbol in Celtic design throughout Ireland and Europe. The spirals, together with other geometric designs, were ordinary in the La Tène period (from roughly the fifth through the first centuries B.C.); art from this period was seldom figurative—human and animal forms did not frequently appear until after the extend of Christianity.

No one seems to be sure how long the terrorist group known as HYDRA has been operating within S.H.I.E.L.D.'s ranks. But today, they made their presence known when they destroyed S.H.I.E.L.D. headquarters, the Triskelion." ― WHiH World News Reporter [src]

Some of the connotations include life-death-rebirth, mother-father-child, past-present-future, spirit-mind-body, and power-intellect-love, to name but a few.