Forgive my elementary explanation, there is probably more to it than this but---
The reactance of the capacitor which decreases with an increase in frequency, will allow only higher frequencies to pass through to the tweeter.
The reactance of the inductor, which increases with increased frequencies, will only pass low frequencies to the woofer.
As far as the 2nd order network, the parallel inductor and capacitor would appear to filter even further, allowing only selected frequencies to reach the woofer & tweeter?
If you're looking for math, baby, don't come looking for me.
