Banana peels turn black in the refrigerator due to enzymatic browning, a reaction triggered by cold temperatures that damages the cells and releases enzymes that react with oxygen. This process is similar to what happens when you cut an apple and it turns brown.
Bananas are tropical fruits, and their cells are not adapted to withstand cold temperatures. When you refrigerate a banana, the cold damages the cell structure of the peel. This damage releases enzymes, particularly polyphenol oxidase (PPO), from the cells. These enzymes then react with naturally occurring phenolic compounds in the peel, as well as oxygen in the air. This enzymatic reaction leads to the formation of melanins, which are brown or black pigments. The green banana peel contains chlorophyll, which degrades and reveals the yellow pigments underneath as the banana ripens. The blackening is simply the enzymatic browning process occurring on top of the yellow peel. The fruit inside the banana is protected by the peel and is less affected by the cold, at least initially. However, prolonged refrigeration can eventually affect the texture and flavor of the fruit itself.
To slow down the browning process and extend the shelf life of bananas, store them at room temperature away from direct sunlight and other fruits that produce ethylene gas, such as apples. If you want to refrigerate ripe bananas to further extend their shelf life, consider peeling and freezing them for use in smoothies or baking.