A double knock in (daki) is a European vanilla option with two American barriers, one of which is set above the underlying asset and one of which is set below it. That means that one of the barriers is a regular barrier (i.e., it can only be hit as the option moves out of the money) and one is a reverse barrier (i.e., it can only be hit as the option moves in to the money).
If during the option's life the barrier:
Either of the two barriers is hit, the payout is that of the underlying vanilla option.
Neither of the two barriers is hit, the underlying option is not activated and there is no payout.