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}.
System with memory : 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}.