Balanced output has the signal (+), its inversion (-) and a ground. The idea is that the same noise is added to the inverted signal, and when at the receiving end the inverted signal is inverted again (so it becomes same as the standart signal) and added to the positive signal, the noise is cancelled. For example, you have a signal +2V, then the inverted signal is -2V. Suppose the signal is propagating on the cable and due to an external noise, 0.5V noise is applied to both + and - signals. So one becomes 2V + 0.5V = 2.5V, and the other becomes -2V + 0.5V = -1.5V. So when you invert the - signal again and add to the + signal. 2.5V + 1.5V = 4V, so the noise is cancelled. For our case, DAPs what is important is that the signal is doubled.
The problem with balanced to RCA connection is that, if the (-) (inverted signal) is connected to ground, it is a short circuit of the half of the amplifier drawing high amounts of current from the amplifier, which can damage it. We have to make sure that, none of R- and L- is shorted to the ground pin: