The inciting incident is an event that disrupts the established normal and kicks off the main storyline. It will usually appear as an opportunity or a problem (or both) for the protagonist. And even if the protagonist initially refuses it, he must eventually address it.

For example, the inciting incident in The Hobbit is when Gandalf arrives and invites Bilbo on an adventure. It disrupts Bilbo’s ordinary life, and while it is presented as an opportunity, Bilbo views that opportunity as a problem (respectable Hobbits don’t go on adventures). He refuses the invitation initially, but later accepts it. If it weren’t for Gandalf’s invitation, the plot in The Hobbit wouldn’t have happened.

The purpose of the inciting incident is to start the main plotline.