Veganism isn't hard to understand. It's really simple to understand the morality of being vegan. Veganism excludes using other animals for our own personal gain: like for the pleasure of food to eat, entertainment like circuses, or clothes to wear.
Pretty simple so far, right?
Just leave the animals alone and only do things that help them.
Sounds simple enough putting it that way :)
Don't participate in any of the behavior that involves their harm, treating them like property, or where we only "help" them to satisfy our own personal gain (like making money off of them in some way).
This means vegans are not involved in supporting or participating in:
exploiting animals
enslaving animals
harming animals
violating animals
taking the lives of animals
This includes not:
eating them (no eating of flesh, i.e. meat/muscle)
eating what they produce (no eating/drinking milk, cheese, eggs, honey, etc.)
eating other by-products that come from their deaths (no eating gelatin, etc.)
using what comes from them (no using wool, fur, leather, etc.)
Veganism recognizes our fellow kin from the animal kingdom as having their own lives which we have no right to harm or take. They are fellow animal beings. We have no right to violate them by taking their lives or their freedom.
Any questions? :D
Be healthy, be moral, and thrive in life knowing you don't partake in direct and avoidable harm towards other fellow animals from the animal kingdom we belong to :D