National elections is when Members of Parliament are elected and a Government is formed. The leader of the winning party becomes the Prime Minister. Local elections are when local Councillors are elected. Again the people who wish to be elected declare themselves, they usually then stick leaflets through your door in the run up to election day. On polling day people go to a polling station and put an X by the name of the person they would like to be their local councillor. The person with the most votes wins, the party with the most amount of councillors becomes the leading party in that area. (Usually a town or area). The councillors are the people that make decisions on local issues, eg new roads, planning applications, taxi fares etc.