Butted tubing is a tube that its walls are thicker toward one end. Double butted is if the tubes walls are thicker on both end, and triple butted is when the tube wall has 3 levels of thickness along its length..

Typically you would use a thicker wall in areas such as the bottom bracket where most forces are created, and leave the middle of the tube thin walled for saving weight..

Here is a nice description on how Reynolds makes butted tubing..