Are you referring to the prioritiy of night actions or priority as in "P1" for sign-ups?
If the latter, it is simply a reflection of how many games one is currently playing in. As in, P1=Priority 1=Currently in no games. Priority 2 means you are playing in one game, and so forth. Standard and Beginner games always give Priority 1 players preference over their Priority 2 counterparts. Also see the forum rules for an explanation.
If the former, it simply refers to which night actions are enacted first. So, if one night kill has higher priority than another night kill and the users of those actions kill each other, the one with higher priority will succeed. Similarly, if two roleblockers (roles which force their target to fail their action, also called hookers) target each other, only the one with higher priority will succeed.
Hope that helped. If you somehow meant something other than what I addressed, feel free to say so.