Application Management function is your "place" where the expertise regarding application you use is "located". This means that such function will have your best application experts on disposal. What's the use? In incident resolution, root cause analysis (Problem Management process), change evaluation/assessment and planning...etc. So, whenever you need experts for applications in use (and, we use a lot of them throughout our working day) - you should know where to look for them.
Now, experts are expensive workforce. So, most probably, you'll not use them for incident troubleshooting (except when incident diagnosis is beyond your incident management staff) but for more complex tasks. Service Desk staff (as an example) is usually part of Incident Management process. Application experts are on some further level of support (e.g. 2nd or 3rd, depending how many people you have in IT Service Management).
Read t he articles to learn more:
"ITIL Application Management Function – Custodian of application knowledge" https://advisera.com/20000academy/blog/2014/09/09/itil-application-management-function-custodian-application-knowledge/
"ITIL application management within the service lifecycle" https://advisera.com/20000academy/blog/2014/03/18/itil-application-management-lifecycle-within-service-lifecycle/