Level 1 of Survivor's Instinct regenerates 1 hit point every 12 seconds; successive levels speed that up to every 10, 8, 6 and 4 seconds. Unless the skill is maxed it is not going to make any difference during a fight, but whenever you go to stash loot, trade or talk to NPCs, your hit points could be topped off by the time you are done.
I put one skill point into Survivor's Instinct at level 12, and found it handy once in awhile. I maxed it in the wastelands to use up some spare skill points, and this was pretty much the only healing I needed for the rest of the game (didn't take much damage most of the time).
