The sentence is correct and accurately describes OAuth.
Delegate is just a standard word, look it up on a dictionary. If anything its internal technical definition is precisely in that sentence.
>"First half of what"
The spec, the standard, half of it deals with X, the other half of it deals with Y. Namely one half being how user grants permission to a third party, and the other half being how the third party makes requests to the main data holder.
If you need another definition: OAuth is a three way protocol between users, a service provider, and a third party. A user gives specific permissions to the third party, so that the service provider can share specific resources with the third party, who acts on the user's behalf.
Op didn't say that it's incorrect. I read the article myself as well and wasn't much smarter than before. For better or worse, llms did a much better job explaining it on a high level and then giving technical details if I still wanted to know more.