What's the difference between the Yiddish and Hebrew languages?

1) There is a big difference. Hebrew is basically a Semitic language, similar to Arabic, and Yiddish is basically a Germanic language, similar to German.
However, among Germanic languages, Yiddish is particular because it contains much more words and expressions of Hebrew origin than German (German also contains a lot of words of Hebrew origin).


Hebrew:
"Language family:
Afro-Asiatic
Semitic
West Semitic
Central Semitic
Northwest Semitic
Canaanite
Hebrew"
http://en.wikipedia.org/wiki/Hebrew_language

Yiddish:
"Language family
Indo-European
Germanic
West Germanic
High German
Yiddish"
http://en.wikipedia.org/wiki/Yiddish


2) "Jewish languages are a set of languages and dialects that developed in various Jewish communities around the world, more notably in Europe, West Asia, and North Africa. The usual course of development for these languages was through the addition of Hebrew words and phrases, used to express uniquely Jewish concepts and concerns, to the local vernacular. Often they were written in Hebrew letters, including the block letters used in Hebrew today and Rashi script. Due to the insular nature of many Jewish communities, many Jewish languages retain vocabulary and linguistic structures long after they have been lost or changed in later forms of the language from which they descended. Among the most widely spoken Jewish languages to develop in the diaspora are Yiddish, which has been spoken by more Jews than any other language in history; Ladino, the language of much of Sephardic Jewry for five centuries; and the Judæo-Arabic group of languages which have been spoken in Arabic-speaking lands for nearly a millennium.

Hebrew is the liturgical language of Judaism (termed leshon ha-kodesh, "the holy tongue"), the language in which the Hebrew scriptures (Tanakh) were composed, and the daily speech of the Jewish people for centuries. By the fifth century BCE, Aramaic, a closely related tongue, joined Hebrew as the spoken language in Judea. By the third century BCE, Jews of the diaspora were speaking Greek.

Hebrew was revived as a spoken language by Eliezer ben Yehuda, who arrived in Palestine in 1881. Modern Hebrew is now the official language of the State of Israel. It hadn't been used as a mother tongue since Tannaic times, i.e. since 200 CE. For over sixteen centuries Hebrew was used almost exclusively as a liturgical language, and as the language in which most books had been written on Judaism, with a few speaking only Hebrew on the Sabbath. For centuries, Jews worldwide have spoken the local or dominant languages of the regions they migrated to, often developing distinctive dialectal forms or branching off as independent languages. Yiddish is the Judeo-German language developed by Ashkenazi Jews who migrated to Central Europe, and Ladino, also called Judezmo and Muestra Spanyol, is the Judeo-Spanish language developed by Sephardic Jews who lived in the Iberian peninsula. Due to many factors, including the impact of the Holocaust on European Jewry, the Jewish exodus from Arab lands, and widespread emigration from other Jewish communities around the world, ancient and distinct Jewish languages of several communities, including Gruzinic, Judeo-Arabic, Judeo-Berber, Krymchak, Judeo-Malayalam and many others, have largely fallen out of use.

The three most commonly spoken languages among Jews today are English, modern Hebrew, and Russian, in that order. Some Romance languages, such as French and Spanish, are also widely used. Overall, the language spoken by the largest number of Jews in history is Yiddish, followed closely by English and then Hebrew. This is due to the fact that Yiddish was spoken by the majority of the world's Jews for several centuries of high Jewish populations (13 million by 1939) and because the descendents of Yiddish speakers after the Holocaust split among speaking several different languages (Hebrew, English, Russian, etc) instead of switching to only one language."
Source and further information:
http://en.wikipedia.org/wiki/Jewish_languages


3) An interesting book about Yiddish and its English variant Yinglish is "The Joys of Yiddish" by Leo Rosten:
http://en.wikipedia.org/wiki/The_Joys_of_Yiddish
http://en.wikipedia.org/wiki/Yinglish