Arch Wiki and other sites only explain the first 6 columns in "xmodmap -pke":
However, running "xmodmap -pke" gives me about 10 columns for some keys:
What do those columns mean?
I have Turkish layout that is similar to English, but with Alt Gr modifier for non-english characters (ü, ğ, etc.) and a second layout for Cyrillic. I'm running Fedora 24 KDE.
Your configuration likely has virtual modifiers (a feature added about ten years ago, without completing the documentation).
They have no predefined meanings. Quoting from How to further enhance XKB configuration:
Any key type description can use both real and virtual modifiers. Since real modifiers always have standard names it is not necessary to explicitly declare them. Virtual modifiers can have arbitrary names and can be declared (prior using them) directly in key type definition: