The term refers to analytics that uses first party cookies. These cookies are tied to your domain, so they can’t be used elsewhere. The reason this is valuable, as only you can activate and use them. Whereas with a third party cookie, that third party could activate the cookie elsewhere. This was useful in other ways, for example, Google setting a cookie, then being able to serve ads to those folks.
First party analytics is more respectful to your users, preserves their privacy and data from being used in ways they didn’t expect. And by virtue of that can help provide more accurate data, as many browsers or users limit the placement of third party cookies.