Wanna quick Yiddish lesson? Say ' a herring is a fish''....

Want a quick Yiddish lesson? Say, "a herring is a fish" while pretending to read this:  אַ הערינג איז אַ פֿיש
And use this guy's accent:

You just read a Yiddish sentence meaning... a herring is a fish.

To explain, let's take a step back: As the Jewish diaspora spread through various parts of Europe, their move away from Hebrew as a spoken everyday language paralleled the change of Latin and Old Church Slavonic into Liturgical languages. Hebrew was too holy to be used to talk about milking cows and the cost of lumber.

So, the Jews  developed a version of their local languages to use as their own wherever they ended up. Yiddish is the language used in Central and Eastern Europe. By comparison,Ladino is what they spoke in Spain (e.g., check out the Ladino Hannukah song, Ocho Kandelikas)

Back to Yiddish, it ended up a bit of a mishmosh of languages (Scholars Debate Roots of Yiddish, Migration of Jews) combining not only Hebrew with German, as the other answers have noted, but also Slavic (particularly for Eastern Yiddish, spoken around Russia). In fact, the vocabulary is about 85% German, 10% Hebrew and 5% Slavic. The word Yiddish comes from the German for Jewish: Yid + ish.

The grammar, though, is almost 100% German, or more specifically Germanic. So, Yiddish is a branch of the High German language family. As you may know, English is a also Germanic language, which explains why the phrase a herring is a fish means the same thing in English and Yiddish.

As for the writing system, the learned, of course, still spoke Hebrew in shul or yeshiva (school) and even the illiterate would pray in Hebrew, so Hebrew was a constant influence. Indeed, the Hebrew writing system, known by the literate, was used and modified for writing Yiddish. 

It had to be modified because the sounds are Hebrew and German different and the sounds of German are used. The grammar is different, too, so the Semitic trilateral root, a key part of the grammar, was abandoned in favor of German inflection. The semitic vowel system, related to this grammatical part of the language, was replaced with a different method for writing vowels.

The Holocaust decimated the Yiddish-speaking population, a population that had existed for almost 1,000 years. Those that weren't killed moved to places where Yiddish wasn't relevant. So, Yiddish experienced a precipitous decline. My grandparents' 1st language was Yiddish. My parents knew a little. And I know a few dozen phrase and words. 

But just as Jews are moving back to Germany, so, too, are people starting to use Yiddish again. Some Orthodox Jews in the US, esp. in and around Brooklyn, use Yiddish as a first language - even the kids. The Daily Forward, the paper my grandfather read, still publishes a Yiddish version online and in print: The Yiddish Daily Forward

...though biweekly and not daily.

Time will tell if Yiddish experiences a true revival as a native language, or whether it becomes an interesting historical footnote of Jewish history.