What are the good points of democracy?

This is a very large question that asks a reader to evaluate a complex political system for its merits. I assume you mean "representative democracy", such as the American system of government.

Merits of Representative Democracy:

- The non-elected citizen, who has the greatest to gain and most to lose in a political situation, has the right to determine, by popular vote, their elected leaders. A fair and open election process will guarantee the consent of the voters to be governed.

- The vote gives a citizen power to voice their opinions on a candidate or proposition, thereby meaningfully participating in the society as a whole.

- Representatives provide a citizenry with a specific voice in their government, thereby securing their interests in the legislative process. The representative who doesn't represent their constituency's interests can be voted out of office by that constituency.

- The citizen may petition the government or engage in public protest if they disagree or wish to change a particular part of their government.

- A representative government guarantee certain specific rights of the population. They are legally obligated to perform these duties under punishment of impeachment, imprisonment, or possibly execution (in the case of treason).

- The three branches of government (executive, legislative, and judicial) are balanced so that one branch may not have supreme power over the others. For example, the executive branch may veto a passed bill, but the Congress and Senate may override the veto, making it law. The judicial branch may review the law and find it to be unlawful or unconstitutional, and may strike the passed law down.