1. The capacity to do something: To become a pilot you have to possess the full physical and mental capabilities of doing the job successfully.
2. An aspect of something which is able to be developed; potentiality: Tim was so talented and so musical that he had the capability of entering the music academy abroad.

Even though the house was quite neglected and partly decayed, it had great possibilities and the capability of being rebuilt into a great place!
3. The power of a country's resources to embark on a certain kind of military undertaking: The little, but strong, nation had the capability of producing nuclear weapons.