What are the options for you to use as an egg substitute when you are vegan?
When you are vegan you don’t eat any animal products or by-products. Depending on what you are making and what you are looking for from a taste perspective there are several options for you to substitute eggs. 

Silken Tofu - If you are making a vegan scramble, quiche, or homemade vegan mayonnaise. The creamy texture can help mimic the egg’s soft texture in your breakfast meals and desserts.
Unsweetened applesauce - You can use a quarter cup of unsweetened applesauce for one egg. It adds moisture and sweetness to what you are making. The natural fruit pectin also helps bind the ingredients. It can be dense than an egg in your baking so you may need to use a teaspoon of baking powder to encourage fluffiness. 
Mashed banana - This has a very distinct flavor, so only use it in recipes when you think the banana flavor will complement what you are making. This works well in pancakes, brownies, and banana bread. You can use a ripe medium mashed banana for every large egg. The starches and sugars in the banana help develop a beautiful golden brown crust. 
Aquafaba - This is an ideal substitute for egg whites, giving your dessert structure. Take three tablespoons of liquid from inside your can of chickpeas and whip them to a fluffy consistency. 
Flaxseeds or Chia Seeds - This is best for recipes that don’t require too many eggs. Combine one tablespoon of seeds with three tablespoons of water for every large egg. Let it sit for 20 minutes to get a slimy mixture that mimics and egg.
Baking Soda and Vinegar - Mix a teaspoon of baking soda and a tablespoon of white vinegar together to help create the air bubbles needed in things like pancakes, cookies, and quick breads. This is ideal where two or less eggs are needed.