Potatoes are made of starch, and when they cook, their cells lose moisture, becoming crispy. If more fat is present, the potato's surface will get hotter and more brown.
While oil causes potatoes to brown only by increasing the temperature, mayonnaise triggers the Maillard reaction, which occurs when proteins, sugar, and heat are combined.
Mayonnaise also has a higher smoke point than vegetable oil, allowing you to leave the potatoes in the oven to brown longer without risking them burning.
Because mayonnaise is just a combination of oil, vinegar, and eggs, its flavor dissipates when cooked in the oven. However, it may affect the texture if you use too much.