"better" is an adjective or adverb that you use to compare things. That is a better size. He runs better than I do. "better off" means "in a better situation". It is like a state. Because you are sick, if you stay at home, you will be better off. ==> Because you are sick, if you stay at home, you will be "in a better situation". "better off" is used a lot when talking about finances. If you get a raise at your job, you will be better off. ==> If you get a raise, you will be making more money and your financial situation will be better than before.