most of the time in DSP δ represents an impulse function. your original function contains two impulse functions, one is δ(n+1), it means that is a shifted one (n+1=0), and you can find that is placed at n=-1, the negative impulse is located at n=0.
you say that y is the system's output. That output depends of transfer function of your system and the system's input. Then, if you want to have a more clear understanding of the output, then you need to know the input applied to the system and the transfer function of your system.