The initiation of something is the beginning. It's what sets events in motion, gets the party underway, or kicks off a new program.
An initiation can also be an introduction into something, formally or informally. You might undergo an initiation ceremony when you join the Girl Scouts for the first time, or have a rude initiation into the world of traffic law when you get your first speeding ticket. But beware of the initiation rituals for college frats — you could find yourself swallowing a live goldfish or streaking across campus in your tighty-whiteys.