Democracy is better than a monarchy because it gives the people power to determine how they want to be governed and by whom. A monarchy basically gives power to a single person who rules for his or her entire life before a change of leadership can occur.
A democracy allows the masses to determine how the government is run because it gives people the power to establish and abolish institutions as they deem fit. Democracies also give people the power to choose leaders they deem qualified for the task. A monarchy vests sovereign powers on a single person who can easily become a dictator and mismanage the country.