Double thumbing is an elaboration of the basic right-hand clawhammer banjo technique that enables you to play on the inside strings with your thumb. The ability to do this probably doesn't mean very much to you right now, but double thumbing is a commonly used technique that expands your clawhammer possibilities and comes in handy for all kinds of songs.
Like most other elements of clawhammer banjo, it's pretty easy to play after you practice. (Yes, future double thumbers, you have to practice!)
When you double-thumb in clawhammer style, you're doubling the number of times you play notes with your right-hand thumb. You play not only the 5th string as you would in basic clawhammer style but also the 2nd and sometimes even the 3rd string with your thumb — hence the name double thumbing. Here's a step-by-step guide:
Play the 1st string open with your right-hand index finger, moving down across the string.
Move your right-hand thumb down from its anchor spot against the 5th string and play the 2nd string, moving down across the string.
Repeat Step 1.
Play the 5th string with your right-hand thumb, moving down across the string.
After you've mastered this basic double-thumbing move, try this same technique on the 3rd and 4th strings. When playing a real song, the thumb plays one string or another depending upon which string contains the note you want to hear.
Check out double thumbing on the audio track Clawhammer Double-Thumbing Technique and in the video clip Clawhammer Banjo: Double Thumbing.