The main thing to know about communism is that it is an economic and political system that emphasizes that all people should be equal.
Communism as a formal system came from the ideas of Karl Marx in the mid-1800s. Marx felt that the capitalist system exploited workers unfairly, allowing the owners of businesses to get rich off of the work of the workers. He argued that a proper system would be one in which there would be no rich and no poor people. Everyone would be equal and everyone would have all of their material needs met. This would be accomplished by having the government own all the means of production. The government would then ensure that all people had everything they needed.
Communism, then, is an economic and political system that is meant to ensure that all people are made equal.