A continuous or permanent power supply (also called a Hardwire kit) is a special power supply to permanently power your dashcam. A hardwire kit is used as an alternative to the standard cigarette power supply to be able to use the dashcam in parking mode when the car is parked. This is because most cars do not supply power via the cigarette power supply when the car's ignition is off.
A permanent power supply has a built-in protection that ensures the car's battery does not drain completely when the dashcam is used in parking mode. It interrupts the current when the voltage drops below a certain (sometimes adjustable) point, so you don't have to worry about running out of battery power. Connecting a permanent power supply is preferably done at the car's fuse box.
Detailed instructions on how to install a permanent power supply can be found here.