Capitalism is the dictatorship of the bourgeoisie (people, who control the wealth and means of production - factories, companies, banks). They dictate their will to the proletariat (people working for wage who have no control over how business is run and how profits of their labor are sold), via press/TV/government/police-military actions/lobbying/family ties; many are directly working for the government.

Socialism happens when proletariat becomes the ruling class and distributes the wealth upon all the citizens of the country, providing healthcare, education, housing, enough wage to feed everyone. As proletariat are the majority, socialism becomes a proper democracy, where people can control their own livelihood, not some fat senator who received a 100k 'lobbying gift'.

Communism happens when all the signs of the capitalism vanish (no exploitation of people by other people, no money - goods are produced based on needs and distributed to everyone). It happens when people get rid of bourgeoisie thinking via education and personal experience of having society without hungry, homeless, uneducated people. This happened before (we see slave-owning societies of the past with disgust and feudal states with horror), it just took over several hundred years each time.