Here's my grok of it: Deep learning models progressively abstract a concept presented at the input by passing the input through many sequential layers () until an output layer transforms the output of the final layer into something interpretable, such as an indication of what token to predict next, or a classification, or whatever. The transformer architecture futhermore offers layers that allow different parts of the previous layer's output to sort of mix with each other in complex ways. As you get into greater levels of abstraction, the attention process is mixing very abstract concepts with each other in a nonetheless highly structured manner. I believe this is where the intelligence lives.

sometimes with residual connections, but we can ignore that for sake of simplicity.