Origins
The word 'index' was borrowed into English directly from Latin in the late fourteenth century, initially in the sense of a pointer or indicator. The Latin noun 'index' (genitive: 'indicis') had a wide range of meanings: a forefinger (the pointing finger), an informer (one who points out the guilty), a sign or indication, a title or heading, a list or catalogue, and even the gnomon of a sundial (the part that points to the hour). All these senses are united by the concept of pointing — directing attention toward something.
The Latin word derives from the verb 'indicāre' (to point out, to make known, to declare), composed of the prefix 'in-' (toward, at) and a verbal element related to 'dīcere' (to say, to declare). At the deepest level, the PIE root is *deyḱ-, meaning 'to show' or 'to point out.' This root is one of the foundational etymons of Western vocabulary, producing words across every branch of Indo-European: Latin 'dīcere' (to say — originally 'to point out in words'), 'digitus' (finger — the pointing thing), 'docēre' (to teach — to show how); Greek 'deiknýnai' (to show); Sanskrit 'diś' (direction, quarter); and through Germanic, English 'teach' (from Old English 'tǣcan,' from Proto-Germanic *taikijaną, 'to show') and 'token' (from Old English 'tācen,' a sign).
The connection between the finger, the act of pointing, speaking, and listing is conceptually profound. The forefinger is the index finger precisely because it is the one used to point things out. Numbers were originally shown on fingers, which is why 'digit' means both 'finger' and 'numeral.' A teacher 'shows' students the way (Latin 'docēre,' to teach, is from the same root). A judge 'declares' the law (Latin 'iūdex,' from 'iūs' + 'dīcere'). And an index is a list that 'points to' where things can be found.
Development
The most culturally significant use of the word in Western history is probably the 'Index Librorum Prohibitorum' — the Index of Forbidden Books maintained by the Catholic Church from 1559 to 1966. This was a catalogue that pointed out books Catholics were forbidden to read, including works by Galileo, Descartes, Voltaire, and Victor Hugo. The Index was a list that pointed — and in this case, pointed away.
In the history of the book, the index as an alphabetical reference tool developed gradually. Ancient and medieval manuscripts sometimes had tables of contents ('tabulae') but rarely alphabetical indexes. The modern back-of-book index emerged in the thirteenth century with the development of alphabetical ordering and the introduction of page numbers (manuscript reference by folio number). The index as we know it today — a systematic alphabetical guide to a book's contents — became standard only with the spread of printing in the fifteenth and sixteenth centuries.
Mathematics adopted 'index' in the sixteenth century for a number or expression that indicates a property of another number (as in the index of a logarithm or a power). Economics adopted it in the nineteenth century for a number that tracks relative changes in a quantity over time (the consumer price index, the stock market index). Computing adopted it in the twentieth century for data structures that enable rapid lookup — preserving the ancient Latin sense of a pointer that guides you to what you seek.
Latin Roots
The plural of 'index' has a famous dual form. In technical and scholarly contexts, the Latin plural 'indices' is standard (mathematical indices, economic indices). In everyday English, 'indexes' has become the normal plural (book indexes, database indexes). Both forms are correct; the choice between them is largely a matter of register and convention.