Direct democracy is when the people vote directly on the laws or other issues that are proposed. Indirect democracy is when the people elect representatives who vote on laws on the behalf of the people.
An example of indirect democracy is when we elect people to Congress to represent us.
An example of direct democracy is the initiative or referendum process. This is similar to the process by which California banned gay marriages last year.
In my opinion, many states, especially in the West, could use less direct democracy. California is a prime example. There seem to me to be too many ballot issues and they are generally placed on the ballot by organizations with enough money to pay for signatures to be gathered to get the measures on the ballot. Then people vote for these often complicated measures without having enough knowledge to fully understand the impact of the measures.
So I do not think the average person knows enough to have an informed opinion on most ballot issues. Simple issues, like gay marriage, are okay, but complicated ones are best left to people who have time to become somewhat expert on the issues.