First-party data is information your business collects directly: site visits, form submissions, purchases and calls. A first-party cookie is set on your own domain; a third-party cookie is set by another domain, such as an ad network, while the visitor is on your site.
Browsers have steadily restricted third-party cookies, and some limit even first-party cookies set by JavaScript. Measurement built on your own domain, with server-set cookies and server-side conversion sources, holds up best. It also makes consent simpler, because you control what is collected and when.