These tags (and some other similar ones) are known as "meta-tags": they describe certain aspects of the question that are independent of the mathematical subject the question is about, and they provide some information about what kinds of answer are sought. Their use is considered to be a necessary evil, and is generally discouraged. New users should not create new tags which do not describe aspects of mathematics.
The tags themselves
The use of the tags
The most important thing about these meta tags is that they are meant to convey additional information about the question and not meant to stand alone as tags. In other words, you should never tag a question with only combinations of those four tags above (or other similar ones). For example, a reference-request tag should always be accompanied by a tag for the appropriate mathematical subject the question falls under.
Furthermore, Math.SE is intended, like other sites in the StackExchange network, to be a Q&A website. And we generally prefer questions that have actual answers, rather than questions that are prompts for discussions. (So no "meaning of life" questions here!) When you do ask a question that may not have a single correct answer (as is the case for all big-list questions and some soft-question questions), the moderators encourage you to flag the question for our attention, and we will convert the question to the Community Wiki format which is more suitable for those types of questions.