Democracy
Democracy is rule by the people, usually through some combination of voting, competitive elections, and protections that allow citizens to organise, publish and criticise those in power. Direct democracy has citizens decide policy themselves; representative democracy has them choose officials who decide. The arguments for it appeal variously to the equal standing of citizens, to the quality of decisions reached when many perspectives are heard, and to the possibility of removing bad rulers without violence. The long-standing objections concern the competence and attention of voters, the treatment of permanent minorities, and the gap between an election result and any coherent popular will.
Why it matters
It is the form of government most contemporary states claim to have, so its standards are the ones most governments are measured against.
Where it comes up
Read about Democracy on Wikipedia