An emergency spliff (or emergency joint/blunt) is a spliff you didn't bother finish, so you put it in your pocket for when an emergency comes up, aka. a situation where you just need some high quality dank.
Dude: Oh man, we're going to the cinema to watch Sausage Party later, it sure would be nice with some dank right now
Bro: No worries, i've got an emergency spliff in my pocket!
Dude: Fuck yes