| Hate for hate's sake|
The Jewish question was a topic of debate within Western (primarily European) society over the status, treatment, and place of Jews in society. The term originated in the 18th century in the discussion of the legal penalties and restrictions for Jews that existed in many European states, and whether these should be lifted. In the 19th century, with the development of nationalism, it came to be viewed in this context as one of various "national questions", such as the "Irish question", the "German question", and so on. Through the nationalist lens, the thrust of the question was, are the Jews a distinct nation? Can they be "proper" citizens of the states in which they live? If they are a nation, should they have their own nation-state, and should Jews be encouraged to move there? The modern Zionist movement basically developed to promote the latter; Theodor Herzl's pamphlet Der Judenstaat (literally The Jews' State, often translated as The Jewish State) is subtitled, "Proposal of a modern solution for the Jewish question".
Nazi and neo-Nazi usage
The term has become associated with the Holocaust, which the Nazis often referred to by the brutally mocking name of "The Final Solution to the Jewish Question". This built on the use of the "Jewish question" term by anti-Semitic movements arguing that yes, the Jews are a distinct people, and they are a problem in our countries. From the later 19th century, in Germany as well as other European states, the debate generally oriented around either promotion of Jewish integration and assimilation, or of separating Jews to establish a "cohesive" nation with a single identity, potentially by rounding them up and expelling them. After the Nazis came to power, they began repression of Jews and other "non-Aryans", with part of the goal being to "encourage" Jews to leave Germany. Some did, although they usually had most assets confiscated by the Nazi state, and had difficulty getting other countries to accept them in. Nazi officials explored various plans to forcibly deport Jews, though they never came to fruition. As Nazi control of Europe expanded, some Jews in newly-conquered areas were killed, while others were rounded up into ghettos and concentration camps. Nazi leaders felt the "Jewish problem" was increasingly urgent, and the inability to implement previously-considered "solutions" caused them to move towards the "Final Solution": extermination.
Today, the term has seen revived usage among neo-Nazis and white supremacists, who sometimes refer to it by the initialism JQ. In this usage, it generally is a euphemism for the "truth" that the Jews control the world behind-the-scenes and are working to subvert and eradicate the white race. Gee, I wonder what their "answer" to the question is.