Memoryless system :
Formal Defination : A system is called memoryless if y(t) depends only on an instantaneous value of x(t) not {x(T);T<t} or {x(T);T>t}.
example : y(t)=x(t) + x(t-1) In this example y(t) depends on an instantaneous value of of x(t).
System with memory :
Formal defination: A system is called with memory if y(t) does not depend only on an instantaneous value of x(t) and {x(T);T<t} or {x(T);T>t}.
example : y(t) = x(t+1) In this example ,y(t) depends on a future value of x(t).