Gentleness is the quality of being kind and careful. Your gentleness with a frightened stray dog will eventually convince her to let you feed and pet her.
The noun gentleness is perfect for describing the way someone acts when they are soft and calm and sweet to other people. A good kindergarten teacher speaks to his students with gentleness, and your favorite dentist might be one who treats you with gentleness. The original meaning, from around 1300, was "inherited nature," but by the 1600s it had come to mean "freedom from harshness and violence," with the Latin root gentilis, "of the same family or clan."