With each level of this Perk, you gain an additional 4 Hit Points every time you advance a level. This is in addition to the Hit Points you already gain per level based off of your Endurance.
”— Fallout 2 In-game description
Every time your character gains a level, you gain an additional four Hit Points for each rank of this perk. With two ranks of Lifegiver, that's +8 HP each level, which is more than 10 points in Endurance would give you.
Although it's not clear from the description, Lifegiver grants +4 HP for every level gained, including the level when the perk was taken.
You instantly gain another +20 maximum Health, and slowly regenerate lost Health.
In Fallout 4, this is best as an early-game perk. The math is such that once you reach Level 32, you would have been better off just putting 1 more point into Endurance than in getting a level in the Lifegiver perk. However, the benefits of +20 Health early game can be considerable.
The health regeneration provided at rank 3 does not function in combat (i.e. when there are enemies nearby). The health regeneration gained from the third rank grants the player 0.5% health every second. The health regeneration is fast enough (out of combat) to be a real convenience.