A carter wiring is a 3-way wiring or a multiway wiring method used at the time of old K&T (knob-and-tube) installations, which has been prohibited by the NEC (National Electrical Code) since early 90's.
In carter wiring both phase and neutral lines are connected to the switch. The one throw of the two SPDT switches would be connected to phase line and the other throw to the neutral line. The load or bulb is connected between the common poles of the two SPDT switches.
The light would be OFF when both switches are in the same position, which have either phase or neutral at both terminals of the bulb. When the switches are flipped to opposite direction terminals get opposite polarity and light gets ON.
Unlike from other multiway switching, the two socket terminals would not have fixed phase and neutral points. It changes to either phase or neutral, depends on the switch position.
The carter wiring connection is similar to the H-bridge arrangement used in DC circuits to alternate the polarity of the load.
If the switch position is flipped to phase at both switches, even though the bulb not lights the socket will be charged at both of its terminals. Thus, in this wiring system we can't even replace a bulb by just turn off the light. Because we can't predict whether the socket is de-energized or not. During maintenance a complete isolation of supply line cannot be done by just turning off the light, because we can't make sure it is in a neutral position at both poles. We need to turn off the main switch to ensure an open terminal.
Due to safety issues and high risk of electric shock the carter wiring are no longer recommended wiring system.