Good holiday-cooking question — answering as the UphillTech team:
Fundamentally, the reason for this substitution is that applesauce contains pectin . In baking, the role of oil is to coat the flour, preventing it from combining with the water (or other wet ingredients) and developing gluten . Gluten is what causes dough to rise, and also gives elasticity to the final product - what most people think of as "chewiness." When you're baking, for example, a cake, or even a pie crust, you want to limit the amount of gluten that develops. A cake or pie crust should be moist, light, and fluffy, not tough and chewy. When you bite into a cake and find it very dry...
Full answer by Aaronut: https://cooking.stackexchange.com/a/6875 (CC BY-SA 2.5).
Need help with this? UphillTech.