It reduces damage to you based on the level of the ring and your current missing HP. The effect is mediocre unless either: the ring is high level (5 or 6+) or you're missing a lot of HP. Even then you need the ring at +8 if you want ~50% damage reduction at 50% HP. Compared to just about any other option upgrading tenacity is a poor choice.

Edit: A while back I graphed tenacity and a bunch of other scaling effects to better understand how they scale with upgrades, here's +0 -> +4 and +8:

You can see that the scaling itself isn't terrible (the effect is actually pretty good at high levels) but the effect is pretty mediocre at the levels you'll encounter most often (+0 -> +2.) To get a solidly good effect out of the ring you need to live in the danger zone at fairly low HP, which puts you at risk of getting instagibbed by a surprise attack.

I don't really like the trade offs Tenacity requires but if I were going to play a tenacity dump game I'd be targeting damage reduction equal to missing HP for a given target and then try to stay as close to that level as possible. 50% DR at 50% HP happens at +8, and 70% DR @ 70% missing HP happens at about +9/+10. I'd probably go for +10 then try to stay right at ~30% total HP. The problem is that you're devoting 2/3 (or all with the runes challenge) of your offensive upgrades to just soaking damage and that leaves you with really mediocre damage output.

It is rather a snooze compared to basically all of the other rings. Sure it can reduce the damage you take, but it takes effort to maximize it's benefit.

Consider that it's affect scales with how low your health is. It also applies the reduction after armor and it rounds the result in favor of damage.

This is just a ring you'll wear until you find something better, or transmute it, if it's upgraded.

It's the joke ring. It stands in the joke ring corner, among with elements ring.

You cab make it work with beserker subclass and lots of upgrades. In that case it does make you into a huge tank, and it's a viable choice. Otherwise it isn't worth it.

Hopefully I don't get harrased here for giving an opinion

The ring itself is just straight up, honest damage reduction, both physical and magical.

It's also not your only source of damage reduction, so you stack it on top of other forms of damage reduction, there's a lot of them

Evasion, shields, armor, utility, buffs and debuffs, sustain. All those things are enhanced by the ring of tenacity.

It's kind of the same logic for the warrior Hold fast ability (3-6 armor) and the warden's Barkskin ability ( 0-150% of her level, it goes up to 0-45 armor at level 30)

Even if the Warden blocks significantly more damage, the warrior gets more benefit from the extra armor since he has a passive shield to back it up