The significance of the "agile manifesto" in software development lies in its advocacy for flexibility, collaboration, and customer-centric practices. Established in 2001, the manifesto emphasizes values like individuals and interactions over processes, and working software over comprehensive documentation. This approach allows teams to respond rapidly to changes, adapt to evolving requirements, and deliver software that meets user needs effectively. The agile philosophy has profoundly influenced software development practices, promoting iterative progress and continuous improvement.