stunt_muppet

For the most part, eggs in baking are used as binders for the other ingredients. Now, the reason that works is because of the proteins that the eggs are made up of (because they set up when the water is evaporated, etc), but!!! That protein in and of itself isn’t essential to the action of being a binder in the case of baked goods (generally), just the goopeyness, and there are several good replacements - oil is merely the quickest to hand in most kitchens. Chia seeds soaked in hot water for an hour or so are an eggcellent (sorry couldn’t resist) replacement as well (you should google the amounts, I don’t know them off the top of my head, though I can confirm it works), and there is a vegan powdered egg replacement you can purchase at the grocery store specifically for baking, though I think it really only works well for cookies, imo. Mashed banana is another good binder, so are zucchini, carrots, and a few fruit juices and fatty liquids like coconut milk or blended cashew (which is why banana bread and carrot cake, etc., are such easy recipes to make vegan friendly).
The bottom line is that there are so many interesting options!