With this perk, your radiation level will decrease 1 rad every 20 real-world seconds so long as the player is not currently being exposed to radiation (standing in radioactive water, for instance) - the perk will still be reducing the radiation but the new accumulation of rads will more than overpower the absorption effect. Waiting one in-game hour will remove 6 rads. If you had 999 rads, you would have to wait 167 in-game hours to reduce your rad count to zero. The rate applies to fast travel, sleeping and using the wait function.
This perk is useful in preventing rad build up, which combined with a high radiation resistance can reduce incidences of serious radiation poisoning to few and far between.
Fallout: New Vegas
This perk remains functionally identical to the one in Fallout 3.
However, Irradiated Beauty exists as a possible alternative.