In the example that a bread says it is vegan on the packaging that would mean that there is no animal products such as meat, dairy, or eggs. In the example that someone says that they are vegan that means they eat no animal products at all. This could be for a diet, health reasons, or maybe they just don't want to eat animal products.
Vegan is someone who doesn’t consume any products animal related. This includes meat, milk, eggs, etc. Usually as an alternative they will eat natural alternatives. Tofu is a alternative to meat.
