I have heard this anecdote many times but I don't believe Facebook is actually recording everything we say. Mostly because I don't think our phones have that kind of battery life. I do think they have data on essentially everything you do online.
- They watch how quickly you scroll through the news feed at what you pause on, even briefly.
- They have ad deals with many of the sites you probably visit so can determine many of your search terms and interests even if you didn't search those things through Facebook itself.
- They have your friend & family graph and Facebook messenger context. Even if you personally didn't say something, maybe you mentioned it to a friend at some point and they searched it or discussed it in a chat.
Then we watched a random TV show on Netflix. During the show, two characters discussed a very specific medical method of improving their chances of bearing a child. Literally minutes later, she was getting ads for this type of conception therapy. We are both past child bearing age and have not discussed it in probably 20 years. We had never even heard of the specific type of process. We had never looked it up or read anything about it. It definitely came from something listening to our household, but we don't know what. It was way too specific to have been random chance.
We don't fall into the demographics for such an ad in any way. We have Apple devices with Siri, but that seems unlikely given their privacy policies. We don't have any Amazon or Google home devices (or any other types of their devices). She's on FB, and I'm not, so we think it was probably either her laptop or phone listening. She's had mic access on her phone turned off for Facebook and no other apps were running, but these apps have a way of finding their way around such permissions.
eg - https://www.cnet.com/how-to/disable-vizio-smart-tv-spying/
Once you match the public IP address of all your devices you can link up the identities and do fun advertising stuff.