Agile service management means applying the agile mindset to IT service management, a concept that is as simple as that. Take into account, though, that this is not something that has often been done yet, and as simple as the concept may be, you will be pioneering the effort if you take it on. And even though at first sight, agile sounds quite opposite to the strict ITIL processes, they can work together pretty well.
The agile methodology is created with four foundational pillars in mind. The pillars are built on the core values of agile development, and need only a minor adjustment to also accommodate IT service management: