*Spoiler free version*
You meet Gregg when you die in story mode for the first time.
You cannot die in the story mode until after the tutorial section, you know you have finished the tutorial when the game explains the concept of health to you. (Anti-gravity chocolate)
You meet Gregg the Grim Reaper in story mode when you die for the first time. He explains the concept of "Extra Lives" to you in probably the most comical way possible. "Squirrels can have as many lives as they think they can get away with", if you collect those squirrel tails he will give you an extra chance!
Once you complete the tutorial section of the game, and the concept of health is explained to you (ant-gravity chocolate), you can die.