He's saying that instead of using those red crimp connectors that you should instead solder the two wire ends together and then use shrink tube to insulate the connection. Shrink tube is plastic tubing that shrinks when heated so that you can slide it over a soldered connection and heat it to create new insulation.

However, you said that you still have the original connector that went to the original stereo in the car, right? You should be able to get an adapter for it so that you don't have to solder, crimp, or otherwise mangle the wiring in your car (any more than has already been done). This is by far the easiest way to connect a new stereo to your car. If you can't find anything locally, Crutchfield should be able to provide you with approriate adapters.