Though the Human Rights Act is itself new, its roots go back to the Second World War. After the war, the European Convention on Human Rights (the Convention) was written, setting out important basic human rights. The Human Rights Act now makes the Convention part of British law.
The original rights are set out in separate 'articles'. Since the Convention was written, new 'protocols' have been added. Most of these protocols deal with procedure, but some of them add new rights to the Convention.
Under the Convention, the European Court of Human Rights in Strasbourg was set up for people who thought their rights had been broken ('breached' in legal terms). In many cases, this court decided that the UK government had breached Convention rights, and this lead to important changes in the law in this country.
However, taking a case to the court in Strasbourg takes a long time, and people argued that the Convention would be more effective if it were part of British law, and we could rely on our rights in the British courts. The Human Rights Act was introduced to make this possible.