Serverless computing is a cloud-native paradigm where developers build and run applications without managing infrastructure. It involves short-running, stateless functions that are triggered by events. With serverless, applications automatically scale up or down based on usage, and customers only pay for the compute time used. The document discusses serverless offerings from various cloud providers, demos serverless architectures using Docker containers, and notes serverless is well-suited for event-driven workloads like mobile backends and IoT but not long-running stateful processes.