It has two main components: DNS based and safari extension.
For DNS protection, if you use Apple's native protocol, it uses DoH or DoT to secure your DNS enquiries to your selected DNS server. If you use Adguard's implementation, it will create a pseudo VPN which will filter all connections and block accordingly from the device locally and then pass it on to your selected DNS server.
For Safari extension part, it works almost exactly like the Safari on Mac extension. One is the content blocking API where it sends the blocked domain lists to Safari and the other one is the advanced protection which is used to block complex CSS using javascripts like as in YouTube ads.
If you're really worried, you can just use the content blocking from Adguard and leave the advanced protection off. Though, different websites are hosting the ads on their domains necessitating the use of advanced blocking methods.