The significance of the Agile Manifesto lies in its emphasis on collaboration and flexibility within software development. Established in 2001, it prioritizes individuals and interactions over processes and tools, allowing teams to adapt to change rapidly. Key principles include delivering functional software frequently, maintaining a sustainable pace, and encouraging stakeholder collaboration for ongoing feedback. This approach leads to higher-quality products, as it focuses on continuous improvement and responsiveness to customer needs, making Agile a preferred methodology in dynamic development environments.