Memoryless Systems
A system is said to be memoryless if the output for each value of the independent variable at a given time is dependent only on the input at that very time. It does not depend on past or future samples info.
Example:
y(t)=2(x(t)).
This defines a memoryless system because the ouput y(t) depends on the input,only at time t. Not (t-1) or (t+1).
Systems with Memory
A system is said to have memory when it retains or stores information about input values at times other than the current time.
Example:
y(t)=x(t-3).
This defines a system with memory because the ouput depends on values of future inputs.