Etymology is the study of the history of words. By extension, the phrase "the etymology of [some words]" means the origin of the particular word.
For languages with a long written history, etymologists make use of texts, and texts about the language, to gather knowledge about how words were used during earlier periods, how they developed in meaning and form, or when and how they entered the language. Etymologists also apply the methods of comparative linguistics to reconstruct information about forms that are too old for any direct information to be available.
By analyzing related languages with a technique known as the comparative method, linguists can make inferences about their shared parent language and its vocabulary. In this way, word roots in European languages, for example, can be traced all the way back to the origin of the Indo-European language family.