A double belly buster is a double inside straight draw, meaning that it consists of two overlapping straight draws each missing an inner card.
Example (Texas Hold'em):
Player
Flop
The player has an inside straight draw with 2456, which needs a 3, and with 4568, which needs a 7. This is called a double belly buster. The advantage of this relatively strong draw is that it is not obvious that it has hit.