The character you currently have tagged in would constantly lose a small percentage (usually 1%) of their maximum health every second. Bleeding characters will take 20% more damage per stack of bleed (e.g. with 1 bleed running and with a 1% raditaion, they would lose 1.2% health per second to radiation).
Aquaman/Prime's Atlantean Hero is immune to Radiation. Martian Manhunter/Blackest Night's passive halves Radiation damage like all other forms of damage while his defense buff is active. Blocking while Radiation is active will count toward's Wonder Woman/Prime's passive, despite that the damage is not reduced.