In the world of power supplies, sense wires (also known as remote sense or 4-wire sensing) are used to solve a very specific problem: voltage drop.
When a power supply is connected to a device (the "load"), the wires carrying the current have a small amount of resistance. As the current flows, some of the voltage is "lost" in those wires. E.g. this means if you set your power supply to 5.00V, the device at the other end of the cable might only receive 4.85V. Using sense wires, the power supply will make 5.15V, so compensating for the voltage drop over the output wires.