PHP frameworks like CodeIgniter simplify website development by separating the business logic from the user interface using the MVC pattern. This allows changes to individual elements without affecting other elements, accelerating development. Frameworks save time by avoiding repetitive coding and provide stable applications with effective database interaction and presentation layers. Choosing a framework depends on factors like the intended users, developer experience, and project needs. CodeIgniter is well-suited for projects requiring low overhead, compatibility, and clear documentation.