The two bucket method is exactly what the title suggests, using two buckets rather than one to wash the car. The issue with using one bucket is that you're ultimately transferring the dirt from the car to the bucket and then from the bucket and back to the car. What this means is that the grit particles are being drawn across the paint and causing light swirl marks and fine scratches.
The two bucket method greatly reduces the risk of this happening. One bucket is used for the shampoo solution and the other is filled with clean water. Once you’ve washed a section of the car from the shampoo bucket you then transfer the dirty mitt to the bucket with clean water. You can then rinse the dirt and grit off the mitt, and then transfer back to the shampoo bucket, and repeat. The rinse bucket should also have a grit guard at the bottom which allows the dirt particles to stay at the bottom without being disturbed by the freshly rinsed mitt.
It always amazes me to inspect the rinse bucket at the end of a wash. If you drain it slowly you will see all the grit and dirt collected at the bottom.
Using this method in conjunction with grit guards, wash mitts and drying towels rather than sponges and chamois leathers will greatly reduce the risk of creating light swirl marks and fine scratches in the paint work when cleaning.