Redux-Observable is a middleware for Redux that allows developers to manage asynchronous operations using RxJS operators, enabling the transformation of streams of actions similar to how JavaScript arrays are manipulated. It introduces the concept of "epics," which are functions that take a stream of actions and return modified streams, akin to "sagas" in redux-saga. Through practical examples, the text demonstrates how Redux-Observable can handle asynchronous requests using RxJS's mergeMap() for functions that return promises, with catchError() handling potential errors. By dispatching actions such as 'CLICK_INCREMENT' or 'FETCH_STOCK_PRICE', the middleware modifies action streams, facilitating operations like asynchronous HTTP requests and stock price fetching with node-fetch. This makes Redux-Observable a compelling alternative to redux-saga and redux-thunk, particularly for those familiar with RxJS, and it offers a structured approach to managing async logic in React and Redux applications.