The Sanskrit word 'karma' means action essentially. Karma is generally understood as the result of the action or thought, positive or negative result of each behavior and focus of the theory of samsara, the cycle of rebirths. We can generally say that when the soul leaves the body will reincarnate in a lower or higher being depending on the previous karma. When the karmic residue will be depleted, the atman is free (moksha). Karma is often understood as fate.
|The word 'sanskrit' in devanagari|
More uncertain is the etymology of the word 'atman', another key word of Hinduism. It is often likened to the soul, but really the atman is the Supreme Self, is the essence of every living being, is the Absolute in us that has nothing to do with our personal and individual soul which in Sanskrit is jiva. Perhaps the word from Sanskrit an (to move) and at (breathing), atman being the breath which moves, gives life to every living being.
The 'brahman' however, not to be confused with Brahma one of the three gods of the Trimurti, is the universal principle, the essence of supreme, absolute, pure metaphysical reality. The word is derived from the Sanskrit root brh, which stands for growth and development. In fact everything is born from Brahman and everything is a manifestation of it.
'Avatara' means descent and derives from the Sanskrit root tr / tar 'go' and ava which means 'down'. Then Avatar is going down, down to earth. The avatars are in fact the incarnations of deities with particular reference to the incarnation of Vishnu.