Graphcool is a serverless GraphQL platform used to build production-ready GraphQL backends. It allows developers to create and manage their GraphQL APIs with ease, using its CLI tool. The Graphcool CLI enables users to install the necessary dependencies, initialize their project, and create a GraphQL backend based on a predefined schema. Apollo Client is used to connect React applications to the GraphQL backend, allowing for efficient data fetching and caching. The tutorial demonstrates how to build a simple Instagram app using React, GraphQL, and Graphcool, showcasing the capabilities of the Apollo Client and its integration with the Graphcool platform. Additionally, it introduces GraphQL subscriptions, which enable real-time functionality by subscribing to specific events happening in the backend.