Some people prefer to restrict democracy to mean majority rule by the people, without using elected representatives. That is the definition of direct democracy. In a direct democracy, everyone is entitled to propose policy options and vote on those proposals. The proposals with the most votes become law.
The reference to direct democracy is often used by those who fear the unchecked tyranny of any majority of people. Unconstrained majority rule could indeed create problems for those in any minority – and the founders knew it. Alexander Hamilton said
“It has been observed that a pure democracy if it were practicable would be the most perfect government. Experience has proved that no position is more false than this. The ancient democracies in which the people themselves deliberated never possessed one good feature of government. Their very character was tyranny; their figure deformity.”