A WhatsApp chatbot can be built using Python and the Twilio API for WhatsApp, with the Flask framework being used as a web application. The chatbot needs to define an endpoint that is configured as a webhook so that Twilio can communicate with it. The Flask application defines a /bot endpoint that listens to POST requests, which analyzes the message sent by the user and provides an appropriate response. The chatbot logic involves searching for keywords "quote" and "cat" in incoming messages and returning a quote or cat picture accordingly. Third-party APIs such as Quotable API and Cat as a Service API are used to supply original quotes and cat pictures. The service is run on port 5000, and ngrok is used to allocate a temporary public domain that redirects HTTP requests to the local port. Twilio's WhatsApp Sandbox Settings need to be updated with the ngrok URL, and the request method should be set to HTTP Post.