The phrase "brightest galaxies" refers to the galaxies that emit the most amount of light. They are the most luminous and easy to see among all the galaxies in the universe. Full definition
The cosmos consists of a web of bright galaxies and clusters surrounded by dark pockets that contain little matter. (newscientist.com)
The phenomenon was so unexpected that he conducted an expanded survey, looking at more and brighter galaxy clusters. (discovermagazine.com)
In regards to this, Professor Ohta commented, «This is a big step towards getting the big picture of galaxy evolution as the objects connecting especially bright galaxies in millimeter / submillimeter waves and normal galaxies were detected with ALMA.» (alma-telescope.jp)