It's a crossover/filter. It splits the incoming signal, modifies it and sends the results seperately to the woofer and tweeter, so they reproduce the frequencies that they are designed for.
It may just be a high-pass filter, so it sends the full audio range to the woofer and a truncated signal to the tweeter. You could connect the woofer in turn to each of the outputs (at low volume) and get an idea of what it's doing.
Also just search passive crossover, high-pass filter and low-pass filter and you'll get a proper explanation.