I've seen the term used, multiple times, in comments, as a reason to close a question, and in general I do not disagree with the closure. However, the official reason for the closure is never because "this is a push question."
I have my opinions on what a "push question" is, but providing them would make this a meta push question. It might be useful to have a discussion on what exactly a "push question" is, and why they are bad for this site.
Simply put it is a question that already knows the answer that it is looking for or more specifically is a question that is looking to support the position of that author and does not care about any answers that does not support that belief.
A simplified example of a push question would be asking if something is true and providing evidence of why the author thinks it is true. When it is provided in the question instead of an answer it is perceived as pushing the beliefs of the author instead of looking for an answer even if that answer could turn out to be not what they believe.
The close reason for this ("the primary purpose of this question appears to be to promote or discredit a specific political cause, group or politician") was proposed here. In the simpler terms mentioned there, such questions are a "rant in disguise".
If I were to make finer typology of such questions:
The most obvious case is when someone posts a (really) long question that's largely filled with one-sided arguments in some dispute/controversy. And the question itself is (thus largely) perfunctory to the goal of making their position known in detail. The actual question could be something like "am I right?" It's hard to link to still live questions like this because most get deleted, but here is a meta discussion on one such question (which has some extensive quotes from the original question, so low-rep users can get a clearer idea.)
A less obvious case (i.e. more debatable) is when the question isn't a long rant and actually admits a precise but trivial answer (e.g. something you can find in seconds on Google, or a generic answer that would apply to many other similar situations), but the whole point of the question seems to be to raise awareness to a particular incident, event or occurrence. (To give an [alleged] example, such a question is being discussed here; the question itself is not deleted, but was heavily downvoted. And here is another on a question that was at least in part closed for this reason.)
In general, you can kinda get a feeling that the above two are happening when the OP resists (e.g. rolls back) edits that would make the question shorter (i.e. less of an answer in itself) or not so biased/particularized (if that is actually appropriate).
Another kind of push question is an argument described as a question. Here at politics.se we ask for questions that can be answered objectively, and people occasionally try to sneak in an argument by tacking on an objective question at the end of their post. This question is often just pretence and is superfluous to the rest of the post, and the answer is often obvious or uninteresting.
