Why does Amazon know what I watch on YouTube?

Unless you use an ad blocker (or Pi-hole), you will get served ads when watching a youtube video.

That means:
- you open the Youtube video. That video conveniently has a unique URL, so the Youtube (= Google) server already knows exactly what you're watching
- in the case you have logged in (via Youtube or Google), it also is permitted to access your history and user data over all Youtube/Google sites. Otherwise, it is only limited to your browsing history on that machine through cookies and fingerprinting
- now the video server connects with the ad server (may be the same company, may be different), telling them "we have here user ID John Doe/cookie #12345, give us an ad to show him"
- ad server delivers the ad and notes down that John Doe/cookie #12345 has watched a movie on fly fishing
- now you connect to Amazon and check out some fishing rods. Again, the Amazon server connects with an ad network (assume this is the same, for simplicity here) and tells then cookie #12345 has checked out fishing rods and request an ad to show to you
- next time, you go to Google and search for "holiday trip", Google tells the ad server that John Doe/cookie #12345 is looking for a holiday trip and request an ad to show you. Assuming that this is the same ad network, it knows you have been looking at fly fishing videos, fishing rods and now are looking for a holiday trip, so you'll get both your search results sorted by fishing trips and some ads for fishing trips.

So, yes, at the very least, get an ad blocker. Meanwhile, I am sorely tempted to set up a Pi-hole at home https://pi-hole.net/ - that will also block ads on those systems where I can't run an adblocker (like my phone).

Amazon, google, FB etc share cookie data stored on your device. Thus what one site knows, they all know.

It's to target you with advertising specific to your tastes and needs. All big corporations do it. You don't have to join anything, there are people watching and profiting from people's internet use all the time. I'm not sure the exact mechanism but I'm sure that someone could explain it. The bottom line is that just about everything you do online is being watched by someone and they use this data to target advertising (among other things).

All the tech companies who make money by advertising track what you see. They have agreements with various sites like Yahoo to track everyone. And the government also tracks what you see.

It helps target ads to you.