shadowfaux explained it really well.
Another good way of thinking of Dex is this - you are fighting an enemy who is very fast and likes to dodge all your hits. In order to hit this enemy you need high dex or else you'll just miss. That's what they mean by increasing your "Hit."
Now, lets say you have high dex and now you want to one shot your enemy, that's where str comes in. Dex makes you actually hit the thing and not miss hitting it, while Str makes you hit it hard enough to make it hurt.
That's the metaphor I use when thinking of Dex and Str.