To be "better off" than someone else means that you are in a better situation than they are. In the case above, it does mean that "she" has more money than "I" have.
"Better off" does not have to refer to money, nor does it have to be relative to someone else. For example, you could say "You're better off staying indoors until the rain stops". The opposite of "better off" is "worse off", and it is used in exactly the same manner.
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