Apple created the App Store and iOS for its own devices. They provide a service where they verify that your app is "safe" and they provide "advertising" of your app on the App Store. This makes for a "safe place to find and install apps". So far, so good.
Apple already charges the developer around $100 per year for the ability to submit apps to the App Store. Seems to be a fair price for the security review that Apple performs, so OK.
Now you make your app available and either charge a fixed price and/or have in-app purchases. Apple now starts taking a percentage of the money that people pay in either case. Well, if you're using their payment system that seems fair, but it should be similar to the fee levels that credit cards charge - down in the low percents rather than around 1/3 of the value.
However, Apple have stitched everyone up - you have to use the App Store and cannot use a different payment system and they have pegged their fees at a disproportionate level. (Google have done likewise, but side-loading is possible at the user's risk.)
I don't really understand why governments haven't taken action over this anti-competitive, monopolistic behaviour. It's not like app developers have a real choice here.