What server-side measurement means
In a classic setup, the visitor's browser loads each vendor's scripts and talks to them directly. Every tool receives the request on its own domain, runs its code inside the page and writes its cookies from there. Actual control over what leaves the page is spread across vendors that never consult each other.
The server-side model moves the distribution point. The browser sends a single event to infrastructure you control, hosted under a subdomain of your own website. From there the tagging logic lives outside the browser: that is where you decide which fields are kept, which are trimmed and which destinations they go to.
Two things that often get confused deserve to be kept apart. Collection still starts in the browser, because something has to observe the click or the page view. What moves is the processing and the distribution. Talking about measurement without a browser is therefore inaccurate: the browser stays in the circuit, only with less third-party code and with a single counterpart.
The practical consequence is one of governance. With distribution on the server you can audit in a single place what goes to each vendor, which is very hard to prove when every script decides on its own.