I still don't get it with this virus

Okay so maybe I just don't get it. I'm watching this thing on my Roku TV, Local Now, and there was an advertisement, something about how to stay safe from ppl who are not vaccinated. Like what?? Are they trying to say people who aren't vaccinated are currently infected with the virus and don't know it yet?

No, seriously, I don't understand it. I did have a test back in mid march of 2021 that said I was positive, but I had what would be considered mild symptoms. Then the symptoms went away... but I still carry the virus? Like, that's what it feels like they are saying. That even though I got better, the virus never left my body, and if I dare breathe I WILL 100% infect everyone around me.

Please explain this to me because I honestly don't get it. I don't want your links, I just want a simple, layman terms explanation.