Cycle.js is a functional and reactive JavaScript framework for building user interfaces based on Observables and declarative code. It uses RxJS Observables to model asynchronous behavior and data flow in applications. This allows the unidirectional data flow of views updating models via intents to be modeled as Observables. The document includes code examples of using Cycle.js with RxJS to build reactive UIs, including handling events, updating state, and generating HTML. It also summarizes how the Cycle.run function coordinates driving the application by connecting sources to sinks.