Here is a diagram of a normal simple crossover and the equivalent biamp arrangement. If you follow the signal from the "positive" input it splits - one part goes through part goes through a capacitor (high pass filter) to the tweeter and returns to the negative post. The other part goes through the inductor (low pass filter) to the woofer and again returns to the negative post.
With the biamp setup, one amp supplies the woofer and the other the tweeter so the two speakers are electrically separate. However they both are receiving identical signals and just rejecting the "unused" portion. In fact there is no "crossover".
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