A quango is an organization created by the state, to which the state has delegated state powers and ostensible state responsibilities, instead of leaving this more immediately in the hands of the principal executive part of the state.
For example, an educational quango could be given charge of a school system.
The word "quango" is an acronym for "quasi-autonomous non-governmental organisation". (The acronym is British, so "organisation" is spelled with an "s".)