It means rule by the people. The Greeks who invented the word also invented a way to throw dangerous politicians out of the city for ten years, by writing their names on broken pottery.
Democracy comes from two Greek words: demos, the people, and kratos, power or rule. Rule by the people. It was born in Athens around 2,500 years ago, the first known system where ordinary citizens, not a king, made the decisions.
Athenian democracy was direct. Citizens gathered in person to vote on laws and war. They even had a tool called ostracism: once a year they could vote to banish a man seen as a threat to the city for ten years, casting their votes by scratching his name on a shard of broken pottery called an ostrakon.
It was also sharply limited. Only free adult men who were citizens could take part. Women, enslaved people, and foreigners, the majority of the population, were shut out entirely. The first democracy was real, and it was narrow.
America is not a pure democracy but a representative one, a republic, where citizens elect others to decide on their behalf, with constitutional limits the Athenians never had. The long arc of American history has been the slow widening of who counts as one of the people in rule by the people.