How important is ITIL process in IT Operations Management.?

ITIL ensures the service delivery is archived in efficient manner. with best practices utilization there by creating a process driven environment rather than individual dependent. 

By definition, ITIL is Service Strategy, Service Design, Service Transition, Service Operation, and Continual Service Improvement. If you think about it, IT Operations rely in part or on all of the mentioned stages of processes.

An example: Let's say you are about to outline your strategy on IT Service Continuity when an outage of services occurs. Think about the ITIL stages now I mentioned above. They guide you and create a roadmap of standards steps that help you organize your actions and go through from a strategy, over to a design of a solution, then the necessary transition that incorporates this solution (change management), the following resuming of operation, and the continuous service improvement from lessons learned that help you take note and document in your repository all necessary steps and resources used in order to troubleshoot this case. 

Hope this helps explaining how ITIL can be important in IT Operations Management.