When I check one electrical box in my house, using a multimeter, I get nothing when I touch the black and white wires using the multimeter prongs, but when I touch the black with the ground wire, I get 120 volts. What does this mean and how do I correct it?

You have a serious problem with your Neutral (White) conductor. It may be grounded out (Fault) or fused. You need to find the failure, or get a licensed electrician to find and fix the failure.