A system is Caual if the output signal, at any given time, depends on the input signal only in present and past time. The output signal does not depend on the input signal in future time, otherwise it is considered non-causal.
Example of a Causal System
y(t) = x(t - 10) <-- Y(t) only depends on x(t) 10 units in the past. It does not depend on any time in the future, so therefore it is causal.
Example of a non-causal system
y(t) = x(t + 5) <-- Y(t) depends on x(t) 5 units in the future. Because it depends on the input in a future time, it is therefore non-causal.
