Causal System
A Causal System is a system where the output $ y(t_{0}) $ only depends on the input $ x(t) $ where $ t \le t_{0} $. $ t $ can not be in the future.
Non-Casual System
A Non-Casual System is a system where the output $ y(t_{0}) $ depends on the input $ x(t) $ where $ t > t_{0} $ and may include $ t \le t_{0} $.
