"Endurance is a measure of your overall physical fitness. It affects your total Health and the Action Point drain from sprinting."
As the description says, you'll get more Health for every point of Endurance you have (the number of points vary as you level, and will increase retroactively as you level). The maximum benefit you seem to get from this based on level is fifty points of Health per point of Endurance, which is, quite frankly, an absurd amount. And yes, the Action Point drain reduction while sprinting is another benefit of boosting Endurance, but it's only about 5% per point. Still, on the merits of the Health gain alone, Endurance is one of the more interesting SPECIAL Attributes to boost, perks aside. Which is a good thing, considering the perks in the Endurance tree...
Not starting out strong, Toughness is the physical damage equivalent of Refractor. While you'll suffer far more physical damage than energy damage, ten points of Damage Resistance per rank is still a horrible waste of perks, especially - yes, it's going to be said again - compared to the whopping gains you'll get from investing in Armorer and throwing Ballistic Weave Mk5 in clothing.
Possibly the most useless perk in the game, Bethesda had the nerve to insult your intelligence by offering three freakin' ranks of this garbage. But let's discuss why, exactly, this perk sucks. First, it's easy enough to drop RADS. Use RadAway, visit the decontamination chamber in HalluciGen, or pay a doctor. It's not that dire of a threat. Second, the only time you'll need to eat food presumably is to recover health, which you can do by using Stimpaks, sleeping in a bed, investing in the far, far superior Life Giver perk, or paying a doctor. Third, you can just freakin' cook the animal bits you get from killing critters to remove all RADS! You have many ways to remove RADS, many ways to heal without eating or drinking anything contaminated, and you can just prepare said food at a Cooking Station without investing a single perk.
This perk is possibly the best Endurance has to offer, and it's a pretty decent perk, but the fact that this might be the best really says a lot about the rest of the perks. Anyway, each rank gives +20 Health, which, compared to a single point of Endurance at a high level, isn't very enticing. On the other hand, the third rank also gives you slow health regeneration. It won't save your life in a fight, but it does heal noticeably fast, and between fights, you'll fully heal just by looting, exploring and fast-traveling. It'll greatly extend your exploration and conserve Stimpaks, which isn't a great boon, but once you've picked all the truly great perks, it's pretty handy to grab.
Two ranks, the first of which makes you 50% resistant to addiction, while the second makes you outright immune. Or, alternatively, you could just refrain from chems, save/load before taking them, or visit a doctor on the rare occasion you do get addicted. Caps come easy, perks, well, still fairly easy, but somewhat less easy.
With the first rank in this perk you take no RADS from swimming and can breathe underwater indefinitely, while with the second rank you're undetectable. With this perk, the first rank is all you really need, if you feel inclined to invest in it at all. There are few times you'll need to be underwater for any reason, much less for any length of time (shame there's no secret treasure that can only be obtained with Aquaboy), and the times when you'll be pestered by aquatic foes (Mirelurks) are even rarer. So really, the only reason you'd want this perk is to have peace of mind for when you do go swimming, and to ignore the random RADS you'll catch wading through water here and there. Definitely not a perk you'll want to pay any attention to early on, when much better perks are out there, and honestly, by the time you have everything better, you've probably long since explored everything and have the resources to just pop a RadAway to cure swimming RADS.
Like Toughness and Refractor, you know where this is going. You'll encounter radiation often enough, but it's rarely ever a threat like other forms of damage are, and there are ways to mitigate exposure. Wearing a Hazmat Suit, Power Armor, or popping some Rad-X, for example. At the end of the day, 10 Radiation Resistance is pathetic, and a max of forty Radiation Resistance isn't worth much at all.
Limb damage has never been more uncommon, nor less troublesome than in Fallout 4. Throughout the entire game you'll likely have a limb disabled a handful of times, and to heal it, you need merely wait outside of combat. You'll almost never need to worry about limb damage, much less waste three perks on mitigating it - the exception to this rule being if you get your hands on an Explosive weapon. Explosive Combat Shotguns and Explosive Assault Rifles are beautiful things, but collateral damage is a constant possibility, and this perk will go a long way to reducing frustration while using those weapons.
You can eat corpses to heal yourself! Yum! Or you can just use a Stimpak for healing. Really, aside from role-playing, there's no point in picking this perk. More ranks allow you to eat more things, and it alludes to greater healing as you advance in ranks, but Bethesda's idea of "significant" means "an amount far less than your average Stimpak".
Another lackluster Endurance perk, Ghoulish makes radiation heal you. Cool beans! Except you still take RADS, so while your current health is rising, your maximum health will be decreasing. The rate of healing depends on how many RADS you're taking at the time, so either the healing will be negligible, or entirely off-set by the RADS. Not really a winner of a perk, here.
Another situtational perk akin to Night Person, this perk gives you a bonus to Strength and Endurance (with all attendant benefits), but only during the day. Granted, that's about half the time, and the Endurance boost alone will give you a decent Health boost. Later ranks add Radiation and Health regen during the day, which is actually pretty nice, if unnecessary. At the end of the day, it's not high up on the list of "must-have" perks, as Life Giver does much of the same, but requires far fewer perks to get. On the other hand, if you're super high level, there are worse things to waste perks on than pumping up Endurance for the Health, and enjoying some regen. For most players, however, you'll never have enough free perks to make this appealing, and the regen, while appreciable, is really only a substitute for easily-obtainable RadAway and Stimpaks.