Old High German (Althochdeutsch) is the name given to the language in which some texts were written from AD 750 to 1050, including the earliest known written texts in German.
"German" refers to the language spoken today in Germany, Austria, a large part of Switzerland, and in Luxembourg and Liechtenstein, and by about a million people each in France, Italy and the United States -- by about 100 million people worldwide. "Germanic," however, is a much broader term: in addition to German, the Germanic languages spoken today include English, Dutch, Flemish, Swedish, Norwegian, Danish, Icelandic and others.As I said, the earliest written German texts are Old High German. But they are not the earliest written Germanic texts. In the 4th century, Bishop Ulfilas translated the Bible, or least large parts of it, into his native Gothic language. Also in the 4th century, a few other documents were written in Gothic by Ulfilas and/or someone else. And that is all that is known. For whatever reasons, written Gothic did not thrive.
About a century earlier than Old High German, the earliest known writing in Anglo-Saxon, or Old English, appeared, the poem called "Caedmon" after its supposed author.
Now, about the "High" in Old High German. To this day there are High German and Low German (Plattdeutsch). High German is the standard version of the language usually spoken on TV and radio, written by journalists and authors and so forth. Out of the huge number of local German dialects, High German has come to be standard German. But "High" is not a value judgment. It does not connote anything cultural or social at all. Rather, High German is a purely geographical term: it is so called because it comes from mountainous areas, and Low German from regions where the land is flatter and the elevation is lower.
The earliest Old High German texts are glosses, German synonyms written in the margins of Latin manuscripts, and lists of Latin-synonyms. Then come actual translations, of gospels, of Psalms, of earlier Christian writers, occasionally even of "pagan" Latin Classics. There are official pronouncements of Frankish rulers, pieces of the liturgy, passion plays, magical formulas. There is the Hildebrandslied, a tragic story of a battle between a father and son, a survival of Germanic oral literature.
Old High German was strongly supported by Charlemagne and his successors. Then, as the Saxons took control in German, there was a century, roughly from AD 900 to 1000, when written German virtually disappeared. Latin had been the dominant written language the entire time, but under the Saxons, Latin's status returned from dominant to exclusive.
And then, in the first half of the 11th century, in the period of transition from Old High German to Middle High German, the dominant figure in literary German was Notker, also called Notker the German, to distinguish him from the 9th-century Notker the Stutterer, known for his German additions to the liturgy. In addition to purely German works, Notker the German wrote distinctive mixed works, part Latin, part German.
After Notker, beginning around AD 1050 and lasting until about 1350, is the period of the literature referred to as Middle High German, with authors much more well-known and widely-read than anyone in Old High German: for example, Hartmann von Aue, Gottfried von Strassburg, Wolfram von Eschenbach, and, perhaps the most prominent Medieval German work, the anonymous Nibelungenlied. Old High German is more foreign, more difficult for contemporary readers to comprehend, often comparatively primitive. Still, it offers fascinating glimpses into the life of the times and places where it was made.