The Manage Infrastructure permission is a AppMon Server level permission (note the server image next to the permission in the Role screenshot). This means that this permission does not apply at the System Profile level but the overall server level, see screenshot for User Groups using different Server and System Profile levels. This permission would allow users to modify the host alert thresholds as well as the which external (outside Dynatrace Agent) processes are monitored. I would not suggest giving this permission to average users, only administrators.
Also note that Host or Infrastructure metrics and monitoring is held outside of individual application System Profiles due to the fact that multiple applications (crossing System Profiles) could all be running from the same host, this allows AppMon to only store the host metrics once. The Show Infrastructure permission allows users to view the Infrastructure dashlet from the cockpit.