These adds remind me which goods I've searched recently. Internet knows us...
The Internet doesn't know you. Your PC does. When you do a search on Google, that search is saved locally on your machine in the form of cookies. The next time Google Adsense wants to send you an ad, they look for that cookie, and in many cases will send you an ad based on your last / recent search.
I personally don't like this AT ALL. First, if you share your PC with other people, they see ads meant for you. This can be particularly frustrating when you are searching for a gift for someone, and the next time they use your PC they get spammed with ads for the same item you just bought as a "surprise". My wife doesn't want to see ads for mountain biking, and I don't want to see ads for women's clothing. (This is why Windows has created user accounts, so that each time someone uses a PC, and logs on with their own specific account, they have a personalized experience that involves a LOT of stuff - but includes personal cookies in your web browsers. However many people (like me) don't like having to log out / log in every time you want to do something).
Used to be that I could very specifically tailor which ads were shown to you. This is a gardening site, so I made sure the ads were only for gardening-related products. However Google took that control away from me, and if you look at the ad revenue they were correct at some level - people look at and click the ads based on prior search activity MORE than they click on the ads for gardening stuff. I still don't like how it makes the site look
If you don't like Google "knowing you" just block cookies and delete all cookies (or Google cookies) from your machine. You can create site-specific cookie permissions if you so desire, so that, for example, bonsainut will remember you (and your login info, etc) but no other site will. Then you will see much more generic Google ads - for Walmart, etc. The downside is that the ads will be far less relevant to you, so you are much less likely to care about them (and click on them).
Or... use another search engine. Google can't send you personal ads if you use Bing search, for example. And there are other engines with specific privacy advantages. A search engine called "DuckDuckGo" won't save ANY user search info.