These words refer to the fact of someone being able to do something.
Abilitycan be used in most situations. It is followed bytowith an infinitive.
She's reached the point in her career where she has the ability to do whatever she wants.
He's a great player because he has the ability to see what's coming.
Capacityandcapabilityare more commonly used in writing.
Do you think he has the capacity to do the work?
The tests show that the disease is not affecting her mental capacity.
These small villages don't have the capabiltiy to host the Olympics.
The opposite ofabilityisinability.
His inability to settle down in a job was holding him back.