Cucumber is a tool that supports Behavior Driven Development. It allows writing tests in a simple language called Gherkin that both technical and non-technical team members can understand. The key components of a Cucumber project include feature files written in Gherkin that describe scenarios using keywords like Given, When, Then. These are linked to step definitions in code to execute the test steps. Setting up a Cucumber project involves installing dependencies and creating a standard directory structure with features, step definitions, and support files.