Diodes provide the coding and decoding by phase of the AC current. A diode is put in parallel with the each switch and light.

A diode is a uni-directional valve. It will let current pass in one direction but not the other. A diode in this direction will let positive current pass from left to right but will block negative current. From the other direction negative current will pass but positive current will be blocked. Diodes are marked with the vertical bar to indicate the direction.

At the switches:

When the switch is open, all current is forced to flow through the diode. One switch diode blocks positive current and one blocks negative current. If both switches are open, all current is blocked and no lights light up.

When a switch is closed, the diode is bypassed, shorted out, and both polarities can pass through the switch. Otherwise, each diode blocks one polarity.

At the lights:

The lights act as resistors and will pass both polarities. Here, each diode acts as a short circuit for one polarity, and acts to bypass the light. The other polarity, blocked by the diode, is forced through the lamp and causes it to glow.

With two switches there are 4 possibilities:

open open 0 current
open closed + current
closed open - current
closed closed + and - current

One light turns on from the + current and one from the - current.

Here's a circuit where the lights are replaced with led's. See if you can figure out what should happen.