Having a free and responsible press means that the information given to the ones who vote will not be manipulated and/or censored.
It is extremely important, because otherwise, a population that has been given manipulated information (like propaganda) will continue to support the oppressive regime in place and their votes will be for nothing, since their votes are heavily influenced by those who have the power (money and influence). Without free and responsible press, the population cannot be critical about their government and so, their choices do not reflect true democracy.