This bet is often seen at land casinos and almost never you can use it online. The name of the bet implies the action - in case you win with the bet you have placed, you can repeat the bet by doubling the initial wager.
The reason why the Double bet is a separate bet can be understood when talking about complicated bets like Voisins du zero etc, when it is hard to count how much money you are to bet. The player this time tells the dealer "Double bet" or "Please double" and the croupier does all the work.
This bet can be very profitable if you manage to win two times in a row. Please note that it is only placed after you have own on the initial.
Unfortunately, you will not find this bet at most of the online casinos, as we have mentioned before. However, once in Vegas or anywhere else you can take advantage of it.