Instead of relying on enterprise certificates, AltStore leverages a lesser known developer feature that allows you to use your Apple ID to to install apps you've developed yourself with Apple's development toolkit called Xcode. You are not actually developing apps, though, and instead there is a bit of tomfoolery working behind the scenes.
"AltStore is a fully native, sandboxed iOS application that allows you to sideload apps by essentially 'tricking' your phone into thinking it’s installing apps that you made yourself, when really they can be any apps whatsoever," Testut explains.
Being a supported installation method by Apple, Testut says his scheme is far less fragile than other distribution methods. He also points out that, in theory, it should be difficult for Apple to thwart this—there is no single enterprise certificate that Apple can revoke, because with this process, every user has their own developer certificate.
The caveat is that AltStore requires you to input your Apple ID and password to communicate with Apple's developer servers. Some people might be understandably hesitant to provide that information. However, you can create a disposable Apple ID for the purpose of installing the AltStore.
"I’ve done everything I can to ensure these credentials are handled properly (i.e. it’s never sent to any 3rd party server, only sent directly to Apple for authentication, and then stored securely in the device’s keychain so nothing else can retrieve it), but since it doesn’t matter what Apple ID is provided, you are more than welcome to create throwaway accounts if desired," Testut says.
It's hard to imagine all of this standing the test of time, as both Apple and Nintendo will likely aim to shut this project down. That is an article for another day.