Triple means to multiply by three. If you triple the number two, you get six, and six is the triple of the number two.
In triple, you see tri which means three. You see this prefix in tricycle (three wheels), tripod (three legs), and triplet (three siblings born at the same time). To triple is to increase threefold, just as to double means to increase twofold, quadruple fourfold and quintuple fivefold. In each of these pairs, the former word is Latin based and the latter has Old English origins.