Linkedin Sign-In is an authentication system that reduces the burden of login for users, by enabling them to sign in with their Linkedin account.
Open Graph is a protocol that is used to integrate any web page into the social graph.
OpenResty is a web platform based on nginx which can run Lua scripts using its LuaJIT engine.
Twitter is a 'microblogging' system that allows you to send and receive short posts called tweets.