What is "double clutching?"

To double clutch means simply that you're raising engine RPMs to match your selected gear when downshifting. That is, when you downshift from 4th to 3rd, the engine RPMs won't be much different and your downshift will be relatively smooth with no "lurch." If you downshift from 4th to 2nd however, without double-clutching or bringing the engine RPMs up to match 2nd gear, the rear wheels will lurch and you'll place increased stress on the synchronizers in the transmission.

To double clutch, first depress the clutch and move the shift lever to neutral. Release the clutch and rev the engine to desired RPMs. Depress the clutch once again and shift down to selected gear. Since the engine is already turning at the selected RPMs, the shift will be smoother and you'll save yourself some wear-and-tear.