is "better off" a phrasal verb? No, it is an adjective meaning 'being in a more advantageous position', and is written as "better- off" when preceding a noun.
how should I use it? You will be better off (in the future) if you graduate from high school.
The better-off people live in that part of town. Here "better-off" means (richer)(in a more advantageous financial position).
what's the difference between it and simply using "better"? The meaning can be different (1), or only the grammar can be different (2).
1...He is better than I am. (I am not as good as he is, at whatever we are talking about)
He is better off than I am. (I am not in as advantageous a position as he is)
2...You will be better off if you don't do that. It will be better for you if you don't do that.