Although there many other benefits of agile, and although those provide us with other reasons to try agile, the five essential benefits of agile are:
Rapid Learning - disciplined application of the scientific method to explore the best ways to deliver valuable results.
Early Return on Investment - opportunity to use the results of work starting with the work delivered at the end of the first iteration.
Satisfied Stakeholders - engagement in the process in a way that allows meaningful contributions from all stakeholders.
Increased Control - mechanisms to track/measure and therefore steer the direction that work is going so that it meets goals.
Responsiveness to Change - processes, tools, roles and principles that allow a team and an organization to embrace change rather than reject, control or suffer from change.
These reasons are sufficient and apply to operations work, project work and open-ended research work, whenever humans are involved. The above links take you to more detailed descriptions of each of these benefits.
What are some of the other benefits of agile?