Help me understand voltage X
Va and Vb refer to the input voltages from any two phases  when used in the example showing two phases.

Vx is the voltage at the common point (Cathodes) of the two diodes.
He does not define this (and he should) but you can deduce this from the first pair of equations



ie Vx = Vinput - voltage drop in inductor due to AC current - diode voltage drop.
This corresponds to starting at Vline and transiting an inductance and a diode. The point in his example that matches this is the DC "bus' where the diode cathodes join.