A unit of competency within a competency standard that an industry has agreed is essential to be achieved if a person is to be accepted as competent at a particular level. All units may be core, but in many cases competency at a level will involve core units plus optional or specialisation units of competency. Core competencies are normally those central to the work of a particular industry or occupation.
Source: NCVER 2013, Australia

The most important specific technical competencies required to be acquired by a particular discipline as core competencies to carry out the roles covered by the Competency Development Framework CDF. Core competencies identify the core units of competency within a competency standard that an industry has agreed are essential to be achieved if a person is to be accepted as competent at a particular level. All units may be core, but in many cases competency at a level will involve core units plus optional support, general and personal units of competency. Core competencies are normally those central to work in a particular industry.(Similar definition used by Queensland government)
Source: Wahba 2013, Global