Communism is a political system where a country is run for the people, by the people. All property and industry is communally owned and all profit is shared amongst the people. The idea is 'from each according to his ability to each according to his need' or something along those lines. There is no wealth or poverty, everyone who is able works, and everyone gets an equal share.
In reality, it's a system of government that has not yet worked. When communist revolutions have taken place, the governments seem to end up having a lot in common with dictatorships (which is one individual controlling the country, without being voted in). The USSR is a great example of how badly people can fair under a so-called communist government. Mass executions and imprisonment, harsh laws and brutal law enforcement, and genocide.
Cheerful, yes?
I hope I've got all that right, I feel a bit mushy brained at the moment smile