The significance of the Agile methodology in software development lies in its focus on iterative progress, collaboration, and flexibility. Agile promotes a customer-centric approach, allowing for regular feedback and adjustments throughout the development process. Teams work in short cycles called sprints, which help in delivering functional software quickly and enhancing responsiveness to changing requirements. The methodology encourages cross-functional collaboration among developers, testers, and stakeholders, fostering innovation and improving overall product quality while ensuring that end-user needs are prioritized.