Its voltage rails. Even with NOTHING connected to the speaker terminals (i.e. no current drawn, an open circuit) a power amp can not swing a voltage greater than its rails. If your amp has 35V rails, it can't put out a signal beyond (or even near that, really), without significant distortion. Regardless of the current draw, the voltage fed to the input times the voltage gain of the amp will result in the voltage it wants to swing to. If it can't reach it, you've got clipping (or at least some sort of nasty distortion). If you take one amp that can swing a max of about 25V (80 watts into 8 ohms assuming unlimited current supply) and then passively biamp with another identical amp, your headroom is still only 25V at instantaneous point in time. Say you had a signal that was a 100hz sinewave and a 10khz sine wave summed together. Each sine wave has a peak of 15V before summing. When you add the signals together, the new amplitude of the signal is 30V. If you fed this into two "25V" power amps separately, they both see a 30V signal even if they may be supplying no current at all. The signal will be clipped and you will have distortion. This is why passive biamping doesn't work.
The reason active biamping DOES work is because the signal is filtered before it gets to the power amp. Take a 100hz 15V sine wave and a 10khz 15V sine wave, add them together, separate them again in a crossover, and one amp will get a 100hz 15V sine wave and a greatly attenuated 10khz sinewave (you can calculate exactly how much based on the rolloff of the crossver). So individually, each amp might only see a 15.1V peak instead of a 30V peak. They will also have, just like in the passive biamping situation, more current output by way of TWO transformers rather than only one.
Active biamping A) increases the amps control over the driver because there are no longer any passive components in there, B) reduces intermodulation distortion (the narrower the bandwidth, the less intermodulation distortion there is), and C) also increases the total amount of potential power.
Passive biamping doesn't accomplish A) because you still have passive components in the signal path. It doesn't accomplish B) because both amps still have to amplify a full range signal. It doesn't "really" accomplish C) because you're still limited to the voltage rails of each amp. In short, passive biamping does nothing.