A direct democracy, is democracy in it's purest, most simplistic form. In a direct democractic system every citizen of the state has a vote on the legislation that is being proposed by the government. Direct democracy was first used in the Greek city states, but is too cumbersome, time consuming and impractical to be used as an effective method of governance in modern nation states. However, sometimes for important issues (such as Scottish independence, constitutional change and EU membership) referendums have been used in the UK to give the people a larger stake in the matter. Referendums are the only modern application of direct democracy.
Whereas in a representative democracy, rather than every citizen voting and scrutinising all the legislation in government, citizens in electoral constituencies elect a representative to carry out this role for them. The main difference is involvement, In a direct democracy the people are more invested in the running of the state than they are in a representative democracy.