A React application initializes in the browser through a series of steps that involve bundling your JavaScript files, serving them to the browser, and then rendering your React components into the DOM. Here's a step-by-step breakdown:

1. Development and Bundling: You write your React code using components. This code is then bundled using a tool like Webpack or Parcel. This bundling process transforms your React code (which uses JSX and ES6+ features) into plain JavaScript that the browser can understand. It also combines all of your separate JavaScript files into one (or a few) bundle file(s).

2. Serving the Application: The bundled JavaScript file, along with any HTML and CSS files, are served to the browser via a server. In development, this is often a development server like the one created by Create React App's npm start command. In production, these files are usually served from a static file server or a CDN.

3. Loading the JavaScript: The browser loads the HTML file and comes across the script tag that links to your bundled JavaScript file. It fetches and runs this JavaScript file.

4. React Initializes: Your bundled JavaScript file includes code that runs ReactDOM.render(), which is where React initializes. This function call tells React to render a component (usually the top-level component of your app) into a certain element of your HTML.

   ReactDOM.render(<App />, document.getElementById('root'));

5. React Renders: React renders your components into the DOM. It does this by creating a "virtual DOM" first, diffing it with the current DOM, and then updating the DOM efficiently.

6. React Takes Over: At this point, React has control over the part of the DOM where it rendered your component. Any user interactions that cause changes to state or props will cause React to re-render the necessary components.

This is a high-level overview of how a React application initializes in the browser. The exact details can vary depending on the tools and libraries you're using in your React project.