WSGI and ASGI are two interfaces that sit between web servers and Python web applications or frameworks, handling incoming requests. WSGI processes requests synchronously, sequentially, which can hinder performance, whereas ASGI processes requests asynchronously, allowing them to run concurrently without waiting for each other to finish. This difference in approach makes ASGI more suitable for modern web development, as seen in the example of baking a cake and making frosting, where ASGI allows for simultaneous processing of tasks, resulting in faster overall performance. The Python framework FastAPI is an example of a micro web framework that uses ASGI, which provides out-of-the-box support for asynchronous code and has gained traction due to its speed and excellent documentation.