Well this is a basic doubt.
Let us take an example of a discrete time impulse response of a system as h[n] which has components at n= 0,1,2.
Now my input signal is made of x+x
I know the summation says to shift h[n] by 1 which is h[n-1] and then get output response as
y[n]= x.h [n]+x.h [n-1]
But why do I have to shift this h[n]? Is it because I have a input at x  also? If so then h[n] also has a component at n=1 so why the time shift is required?