With the Lead Belly perk, 50% less radiation is taken every time you drink from an irradiated water source. In Fallout: New Vegas, this benefit extends to all irradiated food and drink.
Because both games rely on the same engine as Oblivion, which used floating point numbers even if the player only saw rounded whole numbers, it is highly likely that a source of water that goes (for example) from "1 Rad" pre-perk to "1 Rad" post-perk is still accurately treated internally i.e. 1 Rad versus .5 Rad.
At high levels this perk may become redundant; RadAway, Rad-X, and apparel with radiation resistance, such as power armor, become more available and readily obtainable.
In Fallout: New Vegas, there is an abundance of clean water, reducing the relative usefulness of the perk, although the benefit is extended to all irradiated food and water.
With the addition of Implant Y-3 in Old World Blues, this perk potentially becomes redundant, though is still available much earlier and for free. This perk also works on food while the implant does not.
“Your digestive tract has adjusted to the weirdness of the Wasteland! Are you sick of stimpaks? Detest chemistry stations and making your own chess, or constantly scavenging for them? Then look for comestibles and water sources throughout the Commonwealth without the usual "distaste"! Take this perk or ones that help you when you use chems (like Chem Resistant or Chemist).”— Fallout 4 Vault Dweller's Survival Guide description
At levels 1 and 2 of this perk, the Radiation Resistance function, which works similarly to Damage Resistance, is applied to reduce the rads received from ingested food and drink. For example a Radiation resistance of 10 (Level 1 of this perk) will reduce the rads in an item that normally delivers 10 rads, by half, to 5 rads. A resistance of 20 (Level 2) will reduce the rads in an item that normally delivers 20 rads, by half, to 10 rads.
The third level of the perk simply eliminates any rads from any ingested item: no rads are shown in the PipBoy, not even "0 rads" is shown.
Taking this perk early on may help out a lot, particularly in a Survival mode game, as most available food (raw or pre-war) carries significant rads, and RadAway is scarce in the beginning of the game. Conversely, this perk has little value for high-level characters, particularly in a non-Survival game, because foods provide only a fixed amount of hit points (whereas stimpaks restore a percentage). However, in Survival mode, this perk is more useful due to the necessity of regularly eating and drinking to stay satiated and hydrated.
The radiation resistance provided by the first two levels of this perk is added to the radiation resistance displayed in the Pip Boy. This is incorrect (and can be misleading), as this specific radiation resistance is only applied to ingested items, and has no effect in resisting environmental radiation or radiation from weapons. [verification overdue]
“Your digestive tract has adjusted to the weirdness of the Wasteland!”