The Council of the European Union is an Institution with a formal legislative role. It is composed of different configurations of national Ministers (one per country). The exact configuration of each meeting depends on the topic under discussion.
The Competitiveness Council (COMPET) aims to enhance competitiveness and growth in Europe through a focus on the internal market, industry, research, innovation and space. Generally, Ireland is represented by Richard Bruton TD, and Sean Sherlock TD.
For more information please see: http://www.eu2013.ie/events/event-items/meetingofcompetitivenesscouncilcompet-20130219/