There are several reasons why you might be tempted to buy a paid mobile game. Some of your favourite big game licenses are releasing new, must-have releases that you'll need to buy to play. Sometimes, if they're indie games, you'll just want to support the developers by buying their game. And then, other times, you will also pay for access to quality. There are a lot of great paid mobile games out there, in terms of graphics, gameplay, story, etc.
There are several types of mobile games that are known as "pay-to-play" games. First, there are direct purchase games. In order to download and play the game, you have to buy it (on the App Store for paid iOS games or on the Google Play Store for paid Android games). Then there is another kind of mobile game, free to download, offering a small period of free-to-play (often a free demo), after which you have to buy the game to continue the adventure. Finally, there are pay-to-win games. This format is simple, you can play for free unless you want to become strong and advance quickly in the game. In this last format, you will have to pay to buy resources, heroes, unlock important advantages, etc.