The battery ground is the wire that runs from the battery neg terminal to the chassis and provides the return path for all your chassis grounds.
Specific spots to check along the power supply route for your amp: the connection between the power wires (+ and -) and the amp, both connections into and out of the under hood fuseholder, the fuse itself, the pos connection to the battery. If all of those are secure and the battery is grounded properly, then you might have aproblem with a loose connection inside the amp. The best way to test that is to wire up everything sitting on your workbench using a short run from the battery + to the amp and the - straight to the battery as well. If you are still having problems, then either your amp or your battery are bad.
Which gets me thinking...have you checked that your battery is good. A bad or going bad battery can cause the problems that you are describing as well. Did you run the system with the car off and run the battery down or some time in the past leave your lights on and have to get a jump. If so you might have done in your battery. Measure the volatge at the battery with a multimeter with the system on and off and with the car on and off. You can put a load on the charging system without using the stereo by turning on the lights. The voltage shoudn't drop hardly at all with the car running and only a tiny bit with the car off. If you are getting a large drop, then you should take your car to AutoZone or PepBoys and have them check the battery. You might need a new one. Doesn't need to be anthing special or expensive, just functional.