The UK Border Agency is responsible for protecting the country's borders and making sure that nobody enters illegally or without the right documentation. Their website gives information about whether you need a visa to enter the UK, and if so what kind and how to apply to it.
All countries have some organisation of this kind. However, the UK Border Agency has become well known because of some very controversial policies on immigration. Several years ago they introduced some changes which made it very difficult for non-EU students to come and study in Britain. The intention was to stop people coming and pretending to study while really trying to work illegally, but the result was that a number of genuine students were unfairly excluded. This has had a bad effect on language schools and the economy, as well as Britain's reputation abroad. Hopefully there will soon be some changes to this policy, but the Border Agency is having other problems at the moment due to staff cuts.