Without paying, Tinder tells you that someone has liked you, but it doesn't tell you who liked you. The only way to match with that person is to organically swipe "like" on them when they're presented to you in the "random" list of people you get shown on the app. It is however tacitly in their interest to not show you the people who have liked you, so you can swipe for a long time without actually getting shown any of the people that liked you. Couple that with the fact that you have a limited number of "like" swipes a day, and you end up in a situation where you can go days without matching with anyone simply because Tinder isn't showing you the people that liked you. So you need to exercise a level of game theory if you want to actually match with people.

Paying for Tinder, in its various tiers, lets you swipe on an unlimited number of people in a day, or, for more money, lets you just see who swiped on you as soon as they swipe "like."

I don't pay for it personally, but if you are paying for it you're saving time and reducing a lot of the (Tinder imposed) friction, so, I get that. I also get why some people might not see the value in Tinder in the first place, but it does make meeting people in a romantic context a lot easier, or at least more streamlined.