A refugium is a 'safe place'. This is usually in a HOB
fuge or in a sump. In most tanks it is a place to grow macroalgae for nutrient export. If the macroalgae uses up the nitrate and phosphate then unwanted algae in the display can't.
Carbon can be beneficial or harmful depending on the tank. Some tanks will benefit from it because it removes certain toxins (what builds up in any tank, toxins from corals, etc.). If you are doing enough water changes and the tank is doing well enough for trace elements and micronutrients to be your limiting factor then carbon can be harmful because it will remove these things.