It's related to the Latin verb tangere (to touch), and it gives rise to many English words, including:
* tactful - having or showing skill in dealing with people in a sensitive way
* tactile - relating to the sense of touch
* contact - the state of touching or being in communication
* tangible - capable of being touched; real or concrete
So, while "tact" itself isn't used much in English, its meaning is very much alive in our language!