Answer:
After the Jews were driven from ancient Israel by the Romans (the "Diaspora") we were a stateless people who pretty much kept to ourselves. In the 18th century, when Napoleon conquered Europe, he allowed Jews to become citizens of the countries in which we lived, if we wished to. As a result, Jews were forced to come to terms with the "modern" world.
A number of us attempted to "reform" Judaism to make it compatible with the world around us in the 18th century. Others clung to their traditions, so (over time) we were divided into Reform and Orthodox communities. Later, feeling that the Reformers had gone too far but that Orthodoxy was simply incompatible with modern life, a group of us established Conservative Judaism. Orthodox, Conservative and Reform Jews are the most common communities.
Since the reestablishment of the state of Israel, some of us have modified our traditions to accommodate this. These are called "Reconstructionists." There are also Jews who define themselves as cultural Jews, but not religious Jews. Some of them have organized themselves into "Humanist" congregations.
Within the Orthodox community, one can find traditional Orthodox, various Hassidic communities, and "Modern Orthodox" congregations.