The "cite" option on a question is an option only shown on Physics SE, Mathematics, Cross Validation, and Mathoverflow. To quote @FranckDernoncourt, the "cite" option is:
To make it easier for people writing research publications or other types of documents to cite Stack Exchange questions or answers. The cite option generates a reference that is easy to cite in TeX, which is often used by researchers (and pretty much always in maths/physics/computer science). I believe the rationale is only showing cite on SE websites that are more likely to be cited in research publications.
And how do we predict the sites most likely to be cited? Couldn't we make this available for all the sites on Stack Exchange?