So what can I get from details?

2Wh33ler

What does the information mean to me?

SummonerNR

Critical Rating is the "chance" that a hit will be "Critical", which deals a lot more damage than regular hit. Critical "Damage" Rating is an adjustment as to "how much" higher damage the critical hit does. These attributes (similar to synergy and mastery adjustments to them) are Numerical in nature now, instead of being Percentage based like they were a long time ago.
As to + or - adjustment to Health and Attack values in your pic, those are the adjustments from that heroes Base value that your Mastery setup has caused them to now be. Think it is the 1st or 2nd Mastery node on the Recoil tree that may have lowered your heroes Health value. While lots of Mastery nodes will cause Attack value to be higher.

2Wh33ler

Thanks, still trying to understand the game and your explanation helps.