"If a cookie is associated with a file requested from the same domain as the page you are viewing, it’s a first-party cookie. A cookie associated with a file requested from a different domain is a third-party cookie. That’s it."
"Notice that the same cookie can be a first-party cookie one moment and a third-party cookie the next. For instance, when you visit twitter.com your browser sets several cookies associated wth the *.twitter.com domain name. In the context of your stay on Twitter these are first-party cookies. If you then visit huffingtonpost.com, Huffington Post requests files from twitter.com and those requests include the same *.twitter.com cookies, which are now third-party cookies."
http://www.ravelrumba.com/blog/third-party-cookies/