Specifically, Apple tried to solve three kinds of problem.
Putting apps in a sandbox, where they can only do things that Apple allows and cannot ask (or persuade, or trick) the user for permission to do ‘dangerous’ things, means that apps become completely safe. A horoscope app can’t break your computer, or silt it up, or run your battery down, or watch your web browser and steal your bank details.
An app store is a much better way to distribute software. Users don’t have to mess around with installers and file management to put a program onto their computer - they just press ‘Get’. If you (or your customers) were technical this didn’t seem like a problem, but for everyone else with 15 copies of the installer in their download folder, baffled at what to do next, this was a huge step forward.
Asking for a credit card to buy an app online created both a friction barrier and a safety barrier - ‘can I trust this company with my card?’ Apple added frictionless, safe payment.
All of this levelled the playing field. You knew you could trust Adobe or EA with your credit card, and you knew you could trust them not to abuse your PC too much. Panic, Rogue Amoeba or Basecamp have accumulated reputations that mean they get trust too, for tech insiders who’ve known about them for years. But what about a random Vietnamese developer who’s made a fun little game about a bird that flaps? The iOS software model removed trust as a problem, and as an advantage for big companies. You still have to hear about the app - the App Store solves distribution but not discovery - but you don’t have to worry about paying for it and you don’t have to worry what it might do to your computer.
There are people who won’t be able to understand the process of looking for an app, differentiating if the source is reliable, and then downloading the app before finally installing it. THen there’s the problem of what to do if it is a malicious app that makes the device unusable.
Avoid payment fraud is another topic altogether.
Curation by the app store makes helps users overcome this problem. There was a time when friends would look for the tech savvy people in their circle to help them to install a software. The app store has made it easier for users to experiment with different apps and for app developers to reach more users without having to build up the trust in the app maker.