A relay uses a small amount of power to control a bigger amount of power. The taillight wire is used to trigger the relay, since it switches on and off with the key. OP tapped into it at the flasher to avoid cutting any factory wiring. The relay then feeds power directly from the battery to the heated gear. The accessory gets power through thick wire that's essentially hooked right to the battery, but the power feed is switched on and off with the key (thanks to the taillight wire and relay).
Here's a diagram of a relay.
You would hook up the switched trigger wire and the ground on the left side to the coil. The battery would be connected to the upper right point, and the accessory would be connected to the middle bottom point, which is a normally-open (not connected) circuit. When you power up the coil circuit (taillight in this case), it acts as an electromagnet and pulls (represented by the dotted line) the relay switch over, connecting the input (the battery) to the middle bottom output (the accessory). The switch moving over to the other contact is the clicking you hear when a relay activates.
Standard automotive relays may or may not have the bottom right point, which is normally-closed. This contact is connected to the battery when the coil circuit is
not powered, and disconnects when the coil gets power (since the switch is pulled over to the other contact). In this particular scenario, there's not a whole lot of use for the NC contact, but it's handy for other things when you want to turn on A and have B turn off automatically.