An HMM is a statistical model that generates observable sequences through a series of unobserved states. It can be visualized as a finite state machine that emits symbols as it progresses through states. HMMs have a strong statistical foundation and efficient learning algorithms, allowing them to handle inputs of variable length. They have been applied to problems like multiple sequence alignment, data mining, and modeling protein domains. However, HMMs also have limitations like many unstructured parameters, an inability to capture long-term dependencies, and not fully representing protein 3D structures.