What do researchers mean by the "priority" of an idea?
The way I use this term, "priority" means "who had this idea first". Of course, everyone can come up and say "hey, I totally had this idea to determine graph isomorphism in quasipolynomial time in 1990", so it is difficult to validate a priority claim unless there is some written material to back it up. But intellectual priority is the former concept; publication dates are just an imperfect way to measure it.

In fields where research is routinely disseminated before formal publication (using arXiv, preprints, or conferences), such as mathematics, there are (in my opinion) fewer possibilities for issues such as "X had the idea one year before Y, but Y's paper was published earlier" or "Y was a peer reviewer and scooped X's idea".