Etymology is the Descriptive Linguistic field of study (as differentiated from the Theoretical Linguistics and Applied Linguistics fields) where the origins and history of particular words within a given language are explored, as well as a particular word in one language's relationship to words from other languages. For the English language there are wonderful online resources on today's internet about the field, such as in Wikipedia, as well as some fairly extensive Etymological Dictionaries. Of course the Oxford English Dictionary goes into great depth on the subject of Etymology for most of it's myriad of entries, though it is a paid subscription service online. Many words have roots which can be traced all the way back to the theoretical Indo-European language families with a surprising degree of confidence.
The English language word "etymology" derives from the Greek ἐτυμολογία (etumologia) which in turn derives from ἔτυμον (etumon), meaning 'true sense', and of course the popular suffix forming - λογία (-logia), meaning 'study of', further from λόγος (logos), "speech, oration, discourse, word"
Part of the value of Etymological study, is that it can add nuances of meaning to words, that might not be apparent from current usage of that word.