Direct democracy involves individuals within a society voting on each issue that arises rather than having representatives making decisions for them. Even though this sounds good in theory, it would be near impossible in large countries.
For example, this system would be difficult to use for federal issues in the United States. Considering that the US has hundreds of millions of people living here, it would take an enormous effort to organize this type of system for each issue. There would need to be poll workers, functioning machines, venues that would be wiling to host elections constantly, etc. By the time this was all organized, the issue that was supposed to be voted on may be out of hand.
This type of situation may be resolved by the government creating a system of organization that allows for voting to take place on a consistent basis.