Democracy is defined as a system of government in which power is vested in the people, who rule either directly or through freely elected representatives.
In the electoral process, the citizens exercise their democratic freedom by voting for an elected representative, electors. These group of electors are called the electoral collage, they are the one who will officially elect a President and Vice President in your behalf.
Voting for mayors, senators, members of the house of representatives are done directly by the citizens. Voting for President and Vice President are done through freely elected representatives, the electoral college.