Karma is the Sanskrit word for "action" or "doing something." It comes from an earlier Indo-European word meaning "to make" or "to do". The idea of karma in Hinduism was that whenever you did anything, it affected your future life (Compare this to Zen Buddhist ideas in China), and especially your reincarnation.
According to Hindu ideas of karma, if you did something good, especially something for other people, you got good karma and this would help you in the future. For instance, if you helped a friend to understand the assignment, you would pile up some good karma that might make sure the teacher asked you only questions to which you knew the answers. On the other hand, if you did something bad, like killing a spider, you would get bad karma, and maybe when you fell down you would scrape your knee. Americans sometimes say, "What goes around comes around."
In Hinduism, people saw your karma as something given to you by the gods, who decided everything that happened. In Buddhism, though, the gods were left out of it, and karma just happened naturally: good deeds lead to good results, just as apple seeds lead to apple trees. In fact, the whole idea of karma - that it matters whether you are good or bad - may not go back much before the beginnings of Buddhism, maybe about 500 BC. Karma may be an idea that came to India from other cultures.
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