Quango is an acronym used especially in the United Kingdom and the Republic of Ireland. Quangos are arms-length bodies funded by government departments but not run by them. They are given power and paid for by government departments.
They were invented because most government departments do two rather different jobs. One is to make policy about how the country should be run, as indicated by laws passed in Parliament. This is called administration. Their other task is to run or operate the policies in action. Examples would be: to run the prison system, to collect taxes, to guard the country's borders, and so on. Quangos were invented to do the second type of task. They are supposed to do some practical job better than a government department could. Of course, if they fail, the fault is theirs, rather than the government department's.