MEMORY LESS SYSTEM
It is defined as a system whose output at 't0' depends only on the input applied at time 't0'.It doesnt take in the previous inputs or the future inputs.For eg.
y(t)= x(t)+t+2
SYSTEM WITH MEMORY
It is defined as a system,whose output at time 't0',depends not only at that particular time,'t0' but also on the previous inputs as well.For Eg.
y(t)=x(t)+x(t-1)
In the above example,The system output depends also on the previous input at time 't-1' ,along with input at time t.