Drop thumb banjo playing is a technique used in the clawhammer style of playing the 5 string banjo. This technique will give you the ability to play more melody notes when playing clawhammer and will vary up your sound from the basic bump-ditty clawhammer rhythm. I would not suggest trying to learn this technique until you have a solid foundation with your basic bump-ditty clawhammer technique.
Drop thumbing is the act of bringing the thumb down to play the 2nd, 3rd, or 4th string after you play a single note with your finger. It changes the bump-ditty pattern to have a rhythmic feel of bump-y-ditty. It adds one more note in the pattern. By bringing your thumb down to play a single note it gives you access to playing melodies that have more notes in them.