We use “able” especially in the structure be able + infinitive. This often has the same meaning as can. There is a negative form unable.
- Some people are able to / can walk on their hands.
- I am unable to / can’t understand what she wants.
“Can” is preferred in the sense of ‘know how to’, and in expressions, like can see, can hear, etc (see can and could 5: with see, hear, etc).
- Can you knit? (More natural than Are you able to knit?)
- I can see a ship. (More natural than I am able to see a ship.)
“Be able” is used in cases (e.g. future, present perfect) where can/could is not grammatically possible because it has no infinitive or participles (see can and could 1: introduction.).
- One day scientists will be able to find a cure for cancer. (NOT … will can find …)
- What have you been able to find out? (not What have you could …?)
- I might be able to help you. (not I might can …)
“Able” is not often followed by passive infinitives.
- He can’t be understood. (More natural than He’s not able to be understood.)
For differences between could and was able, see can and could 2: ability.
For more information consult a good dictionary like Langman, Oxford, Merriam Webster, or Collins.