Narrow AI or 'weak AI' is developed or trained for a specific task with limited context. It is intended for data correlations or pattern identification. Think IBM's Deep Blue and Google's AlphaGo are examples.
Artificial General Intelligence
AGI or 'strong AI' is an intelligence with generalized cognitive abilities which can find solutions to diverse tasks which it is presented with. Though it cannot innovate or think abstractly like a human does.
Artificial Super Intelligence
ASI refers to intelligences surpassing humans and being able to mimic human thoughts, emotions, and cognitive abilities - like coming up with inventive solutions to problems. Think of C-3PO and R2-D2 from Star Wars.