Yiddish was at one time the international language of Ashkenazic Jews (the Jews of Central and Eastern Europe and their descendants). A hybrid of Hebrew and medieval German, Yiddish takes about three-quarters of its vocabulary from German, but borrows words liberally from Hebrew and many other languages from the many lands where Ashkenazic Jews have lived. It has a grammatical structure all its own, and is written in an alphabet based on Hebrew characters. Scholars and universities classify Yiddish as a Germanic language, though some have questioned that classification.
Yiddish was never a part of Sephardic Jewish culture (the culture of the Jews of Spain, Portugal, the Balkans, North Africa and the Middle East). They had their own international language known as Ladino or Judesmo, which is a hybrid of medieval Spanish and Hebrew in much the same way that Yiddish combines German and Hebrew.
At its height less than a century ago, Yiddish was understood by an estimated 11 million of the world's 18 million Jews, and many of them spoke Yiddish as their primary language. Yiddish has fallen on hard times, a victim of both assimilation and murder. Today, less than a quarter of a million people in the United States speak Yiddish, about half of them in New York. Most Jews know only a smattering of Yiddish words, and most of those words are unsuitable for polite company. But in recent years, Yiddish has experienced a resurgence and is now being taught at many universities. There are even Yiddish Studies departments at Harvard, Columbia and Oxford, among others, and many Jewish communities provide classes to learn Yiddish. Many Jews today want to regain touch with their heritage through this nearly-lost language.
Yiddish is referred to as "mame loshn" ("loshn" rhymes with "caution"), which means "mother tongue," although it is not entirely clear whether this is a term of affection or derision. Mame loshn was the language of women and children, to be contrasted with loshn koydesh, the holy tongue of Hebrew that was studied only by men. (And before the feminists start grinding their axes, let me point out that most gentile women and many gentile men in that time and place could not read or write at all, while most Jewish women could at least read and write Yiddish).
The word "Yiddish" is the Yiddish word for "Jewish," so it is technically correct to refer to the Yiddish language as "Jewish" (though it is never correct to refer to Hebrew as "Jewish"). At the turn of the century, American Jews routinely referred to the Yiddish language as "Jewish," and one of my elderly aunts continues to do so. However, that usage has become unfashionable in recent years and people are likely to think you are either ignorant or bigoted if you refer to any language as "Jewish." Likewise, the Yiddish word "Yid" simply means "Jew" and is not offensive if used while speaking Yiddish or in a conversation liberally sprinkled with Yiddish terms, but I wouldn't recommend using the word in English because it has been used as an offensive term for far too long.
It is generally believed that Yiddish became a language of its own some time between 900 and 1100 C.E., but it is difficult to be certain because in its early days, Yiddish was primarily a spoken language rather than a written language. It is clear, however, that at this time even great biblical scholars like Rashi were using words from local languages written in Hebrew letters to fill in the gaps when the Hebrew language lacked a suitable term or when the reader might not be familiar with the Hebrew term. For example, in his commentary on Gen. 19:28, when Rashi comes across the Hebrew word qiytor (a word that is not used anywhere else in the Bible), he explains the word by writing, in Hebrew letters, "torche b'la-az" (that is, "torche in French").
It is believed that Yiddish began similarly, by writing the local languages in the Hebrew characters that were more familiar to Yiddish speakers, just as Americans today often write Hebrew in Roman characters (the letters used in English).
The Yiddish language thrived for many centuries and grew farther away from German, developing its own unique rules and pronunciations. Yiddish also developed a rich vocabulary of terms for the human condition, expressing our strengths and frailties, our hopes and fears and longings. Many of these terms have found their way into English, because there is no English word that can convey the depth and precision of meaning that the Yiddish word can. Yiddish is a language full of humor and irony, expressing subtle distinctions of human character that other cultures barely recognize let alone put into words. What other language distinguishes between a shlemiel (a person who suffers due to his own poor choices or actions), a shlimazl (a person who suffers through no fault of his own) and a nebech (a person who suffers because he makes other people's problems his own). An old joke explains the distinction: a shlemiel spills his soup, it falls on the shlimazl, and the nebech cleans it up!
As Jews became assimilated into the local culture, particularly in Germany in the late 1700s and 1800s, the Yiddish language was criticized as a barbarous, mutilated ghetto jargon that was a barrier to Jewish acceptance in German society and would have to be abandoned if we hoped for emancipation. Yiddish was viewed in much the same way that people today view Ebonics (in fact, I have heard Yiddish jokingly referred to as "Hebonics"), with one significant difference: Ebonics is criticized mostly by outsiders; Yiddish was criticized mostly by Jews who had spoken it as their native language. Thus the criticism of Yiddish was largely a manifestation of Jewish self-hatred rather than antisemitism.