Athens had a direct democracy. There was no parliament, or rather, every citizen belonged to the parliament. All citizens voted personally on every issue.
This works just fine as long as the whole citizenry can fit into one place, but breaks down as soon as your national population is larger than a town.
Modern democracies get around this problem by being representative democracies. The people choose representatives to decide for them, and government becomes the will of the people only by proxy; it is more accurately the will of the representatives. The only modern democracy I'm aware of that attempts to do direct democracy is Switzerland, which has a relatively small population in a tight space.
Thus, weirdly enough, the most democratic nation the world has ever seen was also the world's first; no nation has ever surpassed Classical Athens for maximising the power of each individual. (As long as the individual was an adult male, but that's another issue...)
Some people have thought hard about introducing modern direct democracy. It could be done, using the internet. The United States, or the European Union, or anywhere, could run the same system as Athens, so that every citizen could be given a vote on every issue, everything managed by an elected executive.
I'm not so sure this is such a great idea. It might be equivalent to putting control into the hands of the small number of people who control the media. Too many people will do what they're told by advertising. Certainly most people have their opinions molded by what they're told. Governments which control public access to information know this very well.