The architecture of a typical web application consists of three main layers: the front-end, back-end, and database. The front-end, or client-side, is responsible for user interaction and presentation, utilizing technologies like HTML, CSS, and JavaScript. The back-end, or server-side, handles application logic, database interactions, and server communication using languages like Python or Node.js. The database layer stores and retrieves data as needed, employing systems like MySQL or NoSQL databases, ensuring a cohesive and functional web experience.