Cloud Functions are used to receive and process webhook requests from external sources such as GitHub, Slack, and HubSpot, which can trigger various actions like sending real-time alerts or storing data for later use. Cloud Functions provide a cost-effective way to handle low volumes of events with pricing unbeatable for serverless services. The setup involves creating a cloud function with an HTTP trigger, configuring the webhook URL in the external source's settings, and integrating the application with the desired platform. For example, setting up a GitHub webhook sends relevant data from pull requests or commits to BigQuery, while a Slack webhook processes messages sent in a channel and stores them in BigQuery, and a Hubspot webhook triggers specific conditions within an automation workflow and sends data to BigQuery.