HR is your hit rate. How often you will hit. DR min and DR max are your Damage Rate. The minimum amount of damage, and the maximum amount of damage you can do per hit. (for successful hits, you can still miss and do 0 damage)
As for the dexterity, when you sit to rest, or sleep, you dexterity drops because you can not move well, or at all, when you are doing those actions. Is that the only time you notice abrupt changes?
Well, resting affecting dexterity makes sense. I am/was wearing herbs which I thought might boost dexterity, but they don't always seem to be in effect. The only other abrupt change is my maximum weight allowance, which jumps up and down, usually by 10.
In fact, such cool questions that longer explanations have been added to the Players' Guide, and also the FAQ.
Sunni's explanations are correct. Here's a tad more info. All attributes, including Dexterity, are calculated as needed. They change all the time, under the influence of quite a number of factors. Sunni mentioned sleep/rest, and that's right. Others include what items you're wearing; time of day; day of week; phase of the moon; location of the planets; whether the room you're currently in is a happy place for Good or Evil or Neutral characters; the temperature of the current room; whether you're hungry or thirsty; whether you're tired; and really a bunch of other stuff too.
Usually these changes are displayed on your Attributes tab, but sometimes they happen too quickly for that: for instance, in the middle of a fight. So you should take your displayed Attribute values as measures of proximity, not absolutes; and you should get used to watching how they change under different conditions. This can make a real difference to your decisions.