what exactly is paid media?

In practice, people use paid media to buy speed. Owned and earned take months to build, paid gets you in front of people the day you turn it on - and stops the day you turn it off. That's why a lot of plans use it to test which messages work before putting effort into the slower channels.

anything where you pay for the placement - google and bing ads, meta ads, sponsored posts, display banners, paid influencer stuff. it's usually talked about next to owned media (your site, your email list) and earned media (press, shares, reviews you get for free).