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.