ADP cuts down the recovery time, or delay, after using any action, be it healing, dodging (maybe even spells, haven't tested as I don't have a sorc yet). People who say it doesn't do anything aren't testing it correctly, and they are receiving false negatives. They hear that it speeds up your animations, and it doesn't. It simply lets you regain control of your character much sooner after an action.
You know how you chug an estus, and you just sit there like a duck for like 2 seconds afterwards and you end up just getting hit again anyways? ADP fixes that. At 39 ADP (the agility cap) I can chug an estus almost twice as fast as my dks1 character and dodge out of the way of the next incoming attack. I actually feel very safe healing in boss fights and such. Lifegems become even faster as well. Not only that, but ADP increases your dodge iFrames. At max ADP like I have, I'd say I actually have more iFrames than my dks1 ninja flip ring character.
This is great for casters. This is great for speedy characters. This is great for dual wielders since they can't block. This is great for Strength builds, because you can invest into ADP, invest in less Strength, twohand your weapon and safely roll around, not needing to block. This is great for Shield Turtle players, because you can bring your shield back up much quicker after healing or rolling. It also lets you be a little riskier with your shield since you can lower your shield to regain some stamina, and then snap it back up in a pinch when it's needed.
This is the Godmode stat, and it makes me laugh every time I hear that it's the "new resistance stat" lol.
Also, Attunement increases your agility as well (though not NEARLY as much), but as a caster, if you have both Attunement and Adaptability, you're going to max out Agility and become a god.
I'm happy to see the poll is favoring ADP. There was a stigma against it when this game came out, but I think people are finally coming around and understanding its use. ADP single-handedly removed that "clunky, slow, frustrating" feeling that this game first gave me. I started a new character, killed a couple bosses and pumped a point into dex to wield the Fire Longsword, and then the rest into ADP until the late 20s. I couldn't believe how easy this made the game. I started wearing light armor and got the Chloranthy ring, and my stamina was shooting up the bar like a rocket. I could dish out a ton of 2h attacks, and safely roll away easily, and be back to full stamina in 2 seconds.