The Indemnified Event is the trigger required to claim under an indemnity.
For example, an Indemnified Event may be a situation where a third-party institutes (or even only threatens), for example, an IP infringement claim against the Indemnified Party due to the use of Software that the Indemnified Party supplied.
If you are the Indemnified Party, you want the Indemnified Event to be comprehensive and to occur as soon as the possibility of a claim arises.