Democracy is a big topic, and a complete definition would be quite lengthy. Simply put, democracy is a system of government in which a part of the population or the whole population makes public policy decisions or elects representatives to do so. This involves voting on matters in a direct democracy or electing government officials to make decisions on one's behalf in a representative democracy.
A free press is an essential part of a functioning democracy. Some have even called it the "life-blood of democracy." For the people to best make the decisions for the operation of their nation, they need to be well informed. Furthermore, the press needs to be free from interference from the government. An independent press assures that people can get the information that they need without the influence of private agendas or propaganda. When information is controlled by the government, it becomes possible to manipulate the people for a political agenda. A truly free and independent press assures that the government cannot interfere in the proper dissemination of information. This helps the electorate make informed decisions for their own benefit. History has many examples of tyrants and dictators disparaging the free press or abolishing it in order to maintain their power.
The founders of the United States recognized the necessity of a free press in a well-functioning democracy. That is why freedom of the press is enshrined in the first amendment of the US Constitution.