1. Be able to has a similar meaning to can (or could in the past):
I'm not able to move my leg = I can't move my leg.
However, can is mainly used to express capabilities or aptitudes acquired with time, while be able to refers to temporary or precise abilities or inabilities:
He can't swim, he has never learned how.
He's not able to swim, the swimming pool is closed today.
2. Be able to also allows us to express can in different tenses in the past and the future:
I was able to get to the meeting on time, despite the fact that the metro was late.
You'll be able to use your arm by the end of the month.