The term "historical linguistics" refers to the study of languages as they have evolved from past to present, which often includes periods of time that pre-date the art of writing -- i.e., requiring "reconstruction" of forgotten languages lacking written records, but which gave rise to languages in which texts were (and perhaps still are) written. It all began, as legend has it, with Sir William Jones.
On February 2, 1786, Sir William Jones -- a British judge in India who studied oriental languages and literature -- delivered a lecture in Calcutta entitled "The Third Anniversary Discourse, on the Hindus," in which he outlined his growing belief that certain languages spoken from India to the European Atlantic shores were related by virtue of having a common ancestor, just as Italian and French had evolved from Latin, and English from an older Germanic tongue. His Discourse and other writings ignited an academic interest in the evolutionary history of languages that continues to this day; a key paragraph from his Discourse reads as follows:
The Sanskrit language, whatever be its antiquity, is of a wonderful structure; more perfect than the Greek, more copious than the Latin, and more exquisitely refined than either, yet bearing to both of them a stronger affinity, both in the roots of verbs and in the forms of grammar, than could possibly have been produced by accident; so strong indeed, that no philologer could examine them all three, without believing them to have sprung from some common source, which, perhaps, no longer exists: there is a similar reason, though not quite so forcible, for supposing that both the Gothic and the Celtic, though blended with a very different idiom, had the same origin with the Sanskrit; and the old Persian might be added to the same family, if this were the place for discussing any question concerning the antiquities of Persia.
(The paragraph above is copied from Winfred P. Lehmann's book, A Reader in Nineteenth Century Historical Indo-European Linguistics, originally published in 1967 and now available online. Those who acquire more than a passing interest in historical linguistics may refer to the Reader for information about the development of the field during the century after Sir William Jones.)
The term "Indo-European languages," then, refers to the set of all languages recognized as belonging to one particular 'branch' of the evolutionary 'tree' of languages -- that stemming from the "common source" hypothesized by Sir William Jones and others before him (e.g. Andreas Jäger a century earlier in 1686), now identified as the ancestral language Proto-Indo-European. (The prefix "proto" designates, by convention, an unattested language that has been reconstructed from later evidence.) Just as a larger, older tree branch has smaller, younger branches emerging from it, leading to twigs, some older languages of the past gave rise to newer languages leading up to the present. Modern day "twigs" include American English, Bavarian German, Mexican Spanish, Parisian French, Irish Gaelic, Lithuanian, Czech, Farsi, and Hindi/Urdu, among many others. Older "branches" from which such twigs eventually emerged include Low and High German, Vulgar Latin, Insular Celtic, Proto-Baltic, West Slavic, Old Persian, and Classical Sanskrit, each with their progenitors, contemporaries, and successors.
For more information about Indo-European languages and their evolution, with numerous links to locale maps, see our IE Maps. A recommended reading about historical linguistics prior to Sir William Jones is George J. Metcalf, "The Indo-European Hypothesis in the Sixteenth and Seventeenth Centuries," pp. 233-257 in Dell H. Hymes (ed.), Studies in the History of Linguistics: Traditions and Paradigms. Bloomington: Indiana University Press, 1974.