There are many available definitions of Z (zero volatility) spread e.g.:
"The constant spread that will make the price of a security equal to the present value of its cash flows when added to the yield at each point on the spot rate Treasury curve where a cash flow is received . In other words, each cash flow is discounted at the appropriate Treasury spot rate plus the Z-spread."
"The Z-spread, ZSPRD, Zero-volatility spread or Yield curve spread on a simple mortgage-backed security (MBS) is the flat spread over the treasury yield curve required in discounting a pre-determined coupon schedule to arrive at its present market price."
The purpose of this article is give a visual (graphical) representation of a z-spread. I will go over the procedure of building a graph in excel. This should help your understanding of the z-spread. Towards the end of this article you should see a graph that is similar to: