A transfer case is a part of the vehicle's drivetrain that distributes power to the wheels when you're on slippery surfaces or in low-traction conditions. It is a mechanical device that transfers torque from the engine to the transmission and then to the axles. Transfer cases are designed to allow the driver to select how much torque they want delivered to each axle, which can help with handling and traction.
The transfer case has two main components; a front output shaft and a rear output shaft. The front output shaft connects to an input shaft on the transmission, while the rear output shaft connects to an output shaft on one of your axles, this is where your axle will connect.
When you're driving on dry pavement, all four wheels are driven by their own individual axles. However, when you're driving on slippery surfaces, like snow or mud, the transfer case takes over so that it can distribute power evenly between both sets of axles, since those conditions limit traction.