From what I understand, it is when you let the clutch pedal out in between gears, when it is in neutral. Say you shift from first to second, you would push the clutch in, pull the stick back into neutral, let the clutch out, then push the clutch back in, ans shift into second.
Only some trucks require this kind of shifting, and it is very slow.
It's when you use the heel of foot to control the breaks and the toe of your foot to control the gas in a manual. It is useful for entering and exiting corners at a faster speed, seeing as you can slow down and match the revs for your next shift at the same time. A very useful skill to have.
Double clutching is used on 18 wheelers and older transmission cars. From what I understand, the way the transmission was made and something to do with the syncros do not allow for sloppy shifts like on modern transmissions. What you do is put in the clutch, put the car in neutral, then release the clutch. Then you give it a little blip of gas to match the revs of the next gear that you will be in, push in the clutch, put it in that gear, and release the clutch. If you are good, it will give you near perfect shifts with minimal clutch wear, but it's unnecessary on most modern transmissions.