It means that you're in a better situation. For example, "There is a storm coming so you're better off if you stay inside today." It means that since there is a storm coming, it will be better for you to stay inside. It suggests that your situation will be better compared to some alternative. It's commonly used when two people end a relationship/friendship. "She'he never really appreciated you, so you're better off without him/her."

As an addition to Abby's excellent answers the most literal meaning in "English English" is that you have more money than before. "You will be better off if you save money for a rainy day"

it maybe mean a way of saying "better conditions"

bettre than = in the satisfactory situation than we were be before

it maybe mean a way of saying "better conditions"