Here is a little example to clear up this big 3 confusion
When replacing an exhaust system, the bigger the pipe, the less back pressure there is the faster the air can escape.
When emptying a bathtub full of water, the bigger the drainpipe, the faster the water can leave.
When current is running from one place to another, such as an alternator to a battery the bigger the wire, the more capacity it has for current transfer.
Thus the stock wiring coming from the alternator and going to the battery which is usually 8 gauge, depending on your car, can only handle a certain load, like 100 amps or something (I don't know exact amount). While 0 guage can facilitate up to 300 amps. So if you have an aftermarket alternator producing 250 amps, and you are still using 8 gauge, you will either burn up your wire, or charge your batteries with only 100 amps. You will not be getting the full benefit out of your alternator.
More Current can travel on bigger wires. So if your battery has 1/0 gauge running to the amplifier, and your alternator has 8 gauge running to the battery than the batteries will be losing at most 300 amps while only gaining 100 amps. Causing the batteries to discharge before they can charge. The more a battery has discharged the lower its output voltage. This phenomenon is known as voltage drop. No matter what you are running the Big 3 is a great idea, and is why I won't drive my car with my new alternator in it until my 1/0 gauge arrives in the mail (hopefully tomorrow!!!!). I don't want to have voltage drops.
If I had a picture of the mermaid ejaculating all over the place I would paste it here... you'll have to settle for a mental image.