If you did not get the game early enough (in the case of iOS: prior to version 1.4), you might see ads in your game. People who did own the game in the early days received an ad free experience and a Coin Doubler as a reward after ads were added to the game. People who didn't, need to pay money in order to get rid of the ads (read the part at the very bottom if you're using iOS). One of the options in the Store is to get the Coin Doubler on top of that. The Coin Doubler is an obvious advantage for most speedrunning categories which is why most categories on the leaderboards are divided into the subcategories "With CD" and "Without CD". In other categories where the Coin Doubler doesn't lead to any noticeable advantage, there is no such division.

If you own the Coin Doubler and you haven't figured out how to turn it off/on: You can do that by clicking the switch in the top right corner of your inventory. Lastly, at least on iOS, there is a workaround to see no ads even without buying anything. If you go to your Settings and select Swordigo, you can turn off the option "Mobile Data" and then exit your Wi-Fi. No ads will be present as long as you are on mobile data. However, please keep in mind that the developers from Touch Foo are only two individual game developers and that you can support them by paying for an ad-free experience.