I understand what the component architecture is, I don't understand how it is different from the multi-transclusion model. Can someone please explain?
The difference is that components are used to encapsulate logic and define how a custom HTML element is rendered. Multi-transclusion is/can be a part of a component. It tells where arbitrary text/HTML/... is placed when the component is rendered.
This is especially useful if you want to create a component to layout your application. I think the official documentation is a good example for that: https://docs.angularjs.org/api/ng/directive/ngTransclude#multi-slot-transclusion