Tapatalk basically provides better mobile access to forums. It has dedicated apps for iOS, Android etc and provides direct push notifications via the app when posts are responded to etc. For me nearly all the forums I visit have Tapatalk support and it provides one place to go to check and read (via the app) when I'm on the move.
I notice there isn't a mobile view for the forum currently so its a nice option to consider. I'm not sure what the impact is to a forum owner. The "free" option mentions Advertising Revenue Sharing so not sure if that means you would need to have banner ads on the forum or not.