What is a "lightning connector" for charging?

It should be in the package with the Apple TV.

It is the same cable that ships with iPhones (and some models iPad).

Charge your Siri Remote or Apple TV Remote - Apple Support

The Lightning connector end of the cable plugs into the Siri Remote. The other end has USB and plugs into a computer, or into an Apple USB Power Adapter (wall outlet).

The Lightning connector is the small end of the cable that comes with the Apple TV -- the end that plugs into the Apple TV. See the following for an example: https://www.apple.com/shop/product/MXLY2AM/A/lightning-to-usb-cable-1-m

The lightning connector is the charging cable which you will have received with your Apple device.