Every time I learn a new language, library or framework, I like to form a mental image of how it works and why it works that way. It helps tremendously with being able to provide practical solutions to business problems if you can discern their pros and cons easily.
I don't learn the technical aspects by heart. You will retain them overtime by practicing regularly with the tool. Instead, I focus on the architectural level and I try to understand how everything fits together.
As for React, I think there are three major aspects that one needs to understand well to be proficient with it. They are the virtual DOM, the components and the component's lifecycle.
The DOM represents a document with a logical tree structure. Almost every UI library is represented with a tree structure because it helps with geometrical transformations and property inheritance. React's virtual DOM is a copy of that structure. Because modifying the real DOM is costly (Computing the new UI representation takes time), React executes the manipulation first on its copy, then compare the new and the old versions to determine the most performance effective way to update the real dom.
That means that what you are writing and updating is not the real dom. It does not have the same properties and you should not treat it the same way. That also means that the React philosophy is also universal as the DOM in the browser is very similar in representation to the UI library in other platforms (Which explains React Native). It is still a tree structure but with new types of nodes. Here is a post that explains the virtual DOM in more detail.
The components are each responsible for a section of the virtual DOM, which may contain other components. There are two types of components: classes, and functions. I like the latter as it's often easier to manipulate. With hooks, you can use a function instead of a class as I do now.
As a developer, what you will be doing is create a tree of components that will include your owns and those provided by libraries. These components will accept props as inputs and will return the section of the tree they are responsible for. There are special components called HOC (Higher Order Components) which are functions that will return either your component with new additional props or a completely new component which will include your component as a child.
So where does the business logic fits? In the case of a class component, there are various stages and React.Component class provides you with methods that will be called at each one of the stages. You choose the correct stage based on what you want to do. Some are called only once upon the creation (mounting) and the destruction (unmounting) of your component, other will be called many times when your component updates (triggered by a lot of things). Here is a more detailed explanation.
Using functions make things cleaner. There is no more lifecycle to worry about. You are provided with the props as parameters and you need to return the tree's section. That's it. Now with hooks, you can do the same thing that the class component used to do. hooks are functions that will accept arguments based on the current props and optionally will return objects that can be used inside the functions. Those objects are not created inside the function scope so they won't be destroyed when the function return. I think they get destroyed when the section of the virtual DOM your component is responsible for is destroyed.
So that's it, that is my mental model of what React is. There are a lot of other things like the relation between refs and real DOM, Babel, and JSX. But I think these three are the most important concepts you need to wrap your head around.