Stat screen says "Increases the chance to ward off detrimental effects".
How this actually relates to the game is anyone's guess; most stats are still a mystery (in regards to their actual effect on combat mechanics). But we can assume it has something to do with increasing your ability to resist debuffs, or reduce their duration.
It's for resisting debuffs. For example... Sidious has a 100% healing immunity debuff on his basic attack. But at times, it doesn't happen and you see the unit you attacked pop the word 'resistance'.
So if a debuff is to be casted on you, the dice is rolled based on your tenacity, to see if you can avoid it. (this is calculated after the debuff is bound to happen)
I don't think we can posit exactly how these stats function until the dev's explicitly state as such. For instance, the opposite of Tenacity is Potency. How would this work? Does it just add a straight percentage chance for an effect to occur, or is this a direct counter to Tenacity? Only the Dev's know.
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How this actually relates to the game is anyone's guess; most stats are still a mystery (in regards to their actual effect on combat mechanics). But we can assume it has something to do with increasing your ability to resist debuffs, or reduce their duration.
So if a debuff is to be casted on you, the dice is rolled based on your tenacity, to see if you can avoid it. (this is calculated after the debuff is bound to happen)