If E = Enzyme, S = Substrate, and P = Product; you can think of enzyme catalyzed reactions like this:
E + S <--> ES --> P
The first arrow, pointing both ways, indicates substrate binding, which is reversible. This means substrate can bind and then be either released or converted to product.
Think of a noncompetitive inhibitor as something that messes with the enzymes ability to finish the job (the ES --> P step). ES can still be formed, but we can't progress to P.
Vmax is the highest rate possible for a given situation. Throwing a noncompetitive inhibitor in basically disables the enzymes it sticks to, so Vmax drops.
Km is the equilibrium constant for the E + S <--> ES step. Since ES still forms normally after we throw the noncompetitive inhibitor in, Km doesn't change.
Hope that's useful. Good luck with your studying.