Traditional old toggle switches allow current to flow in the from the hot wire (one of the black wires) through the switch, and out the load side (the other black wire) from the switch to the light. Current flows through the switch when the switch is on, meaning that the circuit is closed/complete. When the switch is off, the circuit is open, and current can’t flow through the switch.
Z-wave switches require power to flow through them all the time (this is how they have power to light up their status LED, and listen for z-wave commands), even when the light is off. For the switch to have power means that the power has to flow through a completed circuit. There’s two ways to accomplish the switch having power…
Most z-wave switches require a neutral (white wire). On these, there are two paths of current flowing through the switch. The flow of current for the light comes in through the hot black wire to the switch, and out the load wire (often – but not always – black) to the light. The flow of current for the switch comes in through the hot black wire to the switch, then out the neutral white wire. This allows current to flow through the switch and power it even when the light is off.
The other way that a few z-wave switches can get their power, which does not require a neutral, is to let a little bit of power trickle through the switch to the light. This means the light always has power (a lot when the light is on, just a trickle when the light is off). This is OK with incandescent bulbs which have high resistance and won’t light up with just a little bit of current. However, with energy-efficient lights like LEDs, this flow of current is enough to make them light up, pulse, flicker, pop on and off, etc., even when they are supposed to be “off”. Lights are not intended to be powered when off, but since smart switches have to be powered, this trickle current for the lights is one way to let the switch have power.