CAN versus TO BE ABLE TO

Both forms are very similar but there are some differences between them. Let's see them:

• CAN is a modal verb (so you can use it to express possibility, permission, ability or prohibition), an auxiliary (you use it for interrogative and negative forms) and defective (no -s for the 3rd person in singular and no infinitive or past participle forms). TO BE ABLE TO is an expression where the verb to be (the auxiliary) is followed by an adjective+infinitive with TO. See the difference:

She can't come with us, can she? but she's able to do it well, isn't she?

• You use TO BE ABLE TO whenever you need a form you don't have with CAN, that is, infinitive or past participle:

I think I'll be able to see you tomorrow or Sorry, I haven't been able to do it yet

• About the meaning there is a slight difference but if you are intereted maybe you should visit this grammar explanation here
  

If you want to practise, you can do these exercises:

• exercise 1: it's connected to the previous explanation about grammar
• exercise 2: for present, past, etc.

I hope it'll be of any help. If you can't understand the difference, please let me know in class.

See you in class.