A talisman is a charm for luck, but its Greek ancestor meant something closer to "finishing the job."
Etymonline traces the word to Greek telesma. In ancient Greek it meant "completion." By Byzantine times it had come to mean "consecration, ceremony," then "religious rite, payment," and finally "talisman." Behind it stands the verb telein, "to perform religious rites, to pay a tax, to fulfill." That verb comes from telos, "end, fulfillment, completion."
Read in order, those senses suggest a path from a completed rite to the consecrated object the rite produced.
The word reached Europe through Arabic. Greek telesma became Arabic tilsam, with the plural tilsaman, Etymonline says. Wikipedia gives the Arabic as ṭilasm, plural ṭalāsim. French took it as talisman, and English borrowed the French in the 1630s.
The first English sense was precise. Etymonline defines it as a magical figure cut or engraved on stone or metal "under certain observances." The figurative sense, anything that produces extraordinary results, appears from 1784.
The Arabic stage was more than a stopover. Wikipedia describes a learned tradition of talisman making in the medieval Islamic world. The 10th-century 'Abbasid mathematician Thabit ibn Qurra wrote that the noblest part of astronomy is "the science of talismans." His work reached Latin through translators including John of Seville, in the 12th century, and Adelard of Bath. Adelard's version says making a talisman needs deep knowledge of astronomy and astrology.
Talismans also appeared in buildings. Wikipedia mentions the Bab al-Talsim gate in Baghdad, whose knotted serpents were thought to protect against enemies, and Tycho Brahe's observatory, Uraniborg, read by some as an astrological talisman.
Wikipedia separates talisman from its near neighbor amulet. An amulet guards against evil, while a talisman brings good fortune.
The telos root survives in other English words. Teleology, the study of final causes, comes from Modern Latin teleologia, coined in 1728 by the German philosopher Christian von Wolff. English has it from 1740. Telos itself entered English in 1904 for an ultimate aim.