NationBuilder is an application that powers websites and community databases. It also enables sharing on Twitter, Facebook and other social networks. After actions like RSVPing for an event or making a donation on a NationBuilder-powered site, you may be prompted to share that action on Twitter and Facebook. If you've not already authorized NationBuilder to access those applications on your behalf, you will have to do so to enable this sharing function. If you authorize your Facebook account, NationBuilder will share the post to your Facebook without you having to leave the site you're on, and enable deeper integration with that site.
These Facebook authorization settings are specific to the site you're using, and NationBuilder will not post anything on your Facebook that you do not authorize.