Can block: third-party apps you've installed, whole categories of apps, websites in Safari, and adult content covered by Apple's Family Controls system.
Cannot block: Apple's system apps. Phone, Messages, Mail, Settings, Camera, Clock and Maps stay available. This isn't an Aura limitation, it's Apple's rule for every app that uses their blocking system, and it's the reason you can always make a call or get a text.
Partially: content inside another app. If a friend sends you a TikTok link inside Messages and it plays there, that playback isn't the TikTok app opening, so the block doesn't catch it.
Some people find this frustrating. It's also the reason Aura is safe to leave on all day. A blocker that could cut off your phone entirely would be one you couldn't trust.