Sorry... I am new here too and was confused by the same thing as well...
When we are talking about score - what is it that is measured? "Character has highest score in this spec" - does that refer to the gear?
I am confused about it because it actually says that for my offspec that I only use for a few solo quests.
I hardly ever use it, when I use it, I'm bad at it and I never consciously collected gear for it.
So - forgive my noobiness - I'm curious what exactly this phrase means - thanks in advance for the info.