Play by Post Role Play forums are when a group of writers (in this case fans of the Sy Fy Show Z Nation) create a character and take turns posting as that character in the setting of the forum.
The general idea is that you join a site and create a character following the rules of the site, and then write out their actions and reactions to events that occur to that character. There are other forms of Role Play on Facebook, Twitter, etc as well, but RP Forums allow much more freedom in the types of characters made, and amount of writing to be done, as well as story arcs.
There are directories for finding Role Play Forums in a wide range of fandoms and original content. http://rpg-directory.com for example.
Z Nation RP is newly opened prequel forum set mainly in Washington and Oregon state with original characters.
When doing a google search I did not find any other forum Z Nation RPs, though there were some on Google, Tumbler, etc.