If you Google for information about "war on third party cookies", you won't get any cool query completions, but you will get a long detailed opinion from Google's AI confirming that there are serious, long-term, and unresolved issues about privacy and advertising.
Advertisers want to know "who you are". Advertising sites generally attempt to protect the privacy of the people who use their sites so advertisers don't "go around" them. Therein lies a bigger problem.
Cell phone companies and most internet service providers have provided "virtual private networks" behind which you make your web requests. However, often, your browser is not configured to hide information that gives away your email or phone number, and there are plenty of voyeurs "out there" who will be happy to stuff that information into a cookie for everyone to look at. The ONLY protection you have is the permissions on that cookie, which includes the site from which the "cookie creation request" originated ... unless that cookie is declared to be persistent (PERSISTENT cookies are themselves ALWAYS third party and are sometimes "called that"). Most cookies are "session cookies" -- useless -- outside of a timed-out single- website visit.
Simplified, persistent cookies are the largest category of third-party cookies, although other kinds exist. Since advertisers can be anywhere in the world AND include foreign governments which may not have your best interests in mind, it is "in your interest" to generally block all kinds of third party cookies.
Advertisers, however, may complain: gee we can't verify that our ad was shown! This claim is BLANTANTLY false. There are many ways to verify whether an ad was shown by use of server-side websockets and many other technologies, including, for that matter, direct display of an advertisement from a third party site, which is permitted by nearly ALL browsers. The problem is that advertisers want "the dope" on you: your address and phone. When you display an advertisement directly from the advertiser's website, they get ONLY a useless IP- address from which you are reading their ad. Just say no to all: "THIRD PARTY COOKIES" in your security settings.
Without this restriction, you have relatively few "controls" on what can happen behind your back. Millions of dollars are spent each year to weasel around what should be a common-sense restriction.