User blog:PolyhedralMatrix102/Question about Cardinals

In Googology I've heard people speaking about "inaccessible" cardinals or ordinals - what are these precisely? I understand what the Church-Kleene ordinal is and what \(\Omega\) is, but what is an "inaccessible" cardinal?

I ask this because I've heard people talking about it here, and it puzzled me.

Answers are appreciated! Thanks!